qanda-logo
apple logogoogle play logo

Calculator search results

Formula
Calculate the integral
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
$$\displaystyle\int { x \cos\left( x \right) } d { x }$$
$1 \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) \right )$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ x } \color{#FF6800}{ \cos\left( \color{#FF6800}{ x } \right) } } d { \color{#FF6800}{ x } }$
$ $ Calculate the integral using the formula of $ \int x \cos^{n}(x) dx =\dfrac{1}{n}(x\sin(x)\cos^{n-1}(x)-(\int{\sin(x)\cos^{n-1}(x)}d{x})+(n-1)\int{x\cos^{n-2}(x)}d{x})$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ \cos ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \left ( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \left ( \displaystyle\int { \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ \cos ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \left ( \color{#FF6800}{ x } \right) } } d { \color{#FF6800}{ x } } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \displaystyle\int { \color{#FF6800}{ x } \color{#FF6800}{ \cos ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ x } \right) } } d { \color{#FF6800}{ x } } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) \cos ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \left ( x \right) - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { 1 - 1 } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Add $ 1 $ and $ - 1$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) \cos ^ { \color{#FF6800}{ 0 } } \left ( x \right) - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { 1 - 1 } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) \color{#FF6800}{ \cos ^ { \color{#FF6800}{ 0 } } \left ( \color{#FF6800}{ x } \right) } - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { 1 - 1 } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Calculate power $ $
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) \times \color{#FF6800}{ 1 } - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { 1 - 1 } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { 1 - 1 } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$\dfrac { 1 } { 1 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { 1 - 1 } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Add $ 1 $ and $ - 1$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \displaystyle\int { \sin\left( x \right) \cos ^ { \color{#FF6800}{ 0 } } \left ( x \right) } d { x } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \displaystyle\int { \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ \cos ^ { \color{#FF6800}{ 0 } } \left ( \color{#FF6800}{ x } \right) } } d { \color{#FF6800}{ x } } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Substitute with $ u = \cos\left( x \right) $ and calculate the integral $ $
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \left [ \displaystyle\int { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \color{#FF6800}{ \cos\left( \color{#FF6800}{ x } \right) } } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \left [ \displaystyle\int { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } d { \color{#FF6800}{ u } } \right ] _ { u = \cos\left( x \right) } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ It is $ \int -f(x) dx = -\int f(x) dx$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \left [ \color{#FF6800}{ - } \left ( \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ u } } \right ) \right ] _ { u = \cos\left( x \right) } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \left [ - \left ( \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ u } } \right ) \right ] _ { u = \cos\left( x \right) } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ The indefinite integral of $ 1 $ is $ x $ . $ $
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \left [ - \color{#FF6800}{ u } \right ] _ { u = \cos\left( x \right) } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \left [ \color{#FF6800}{ - } \color{#FF6800}{ u } \right ] _ { \color{#FF6800}{ u } = \color{#FF6800}{ \cos\left( \color{#FF6800}{ x } \right) } } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Return the substituted value $ $
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( \color{#FF6800}{ - } \color{#FF6800}{ \cos\left( \color{#FF6800}{ x } \right) } \right ) + \left ( 1 - 1 \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) + \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ Add $ 1 $ and $ - 1$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) + \color{#FF6800}{ 0 } \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) + \color{#FF6800}{ 0 } \displaystyle\int { x \cos ^ { 1 - 2 } \left ( x \right) } d { x } \right )$
$ $ If you multiply a number by 0, it becomes 0 $ $
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) + \color{#FF6800}{ 0 } \right )$
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) \color{#FF6800}{ + } \color{#FF6800}{ 0 } \right )$
$ $ 0 does not change when you add or subtract $ $
$\dfrac { 1 } { 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) \right )$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } } } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) \right )$
$ $ Calculate the value $ $
$\color{#FF6800}{ 1 } \left ( x \sin\left( x \right) - \left ( - \cos\left( x \right) \right ) \right )$
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture
apple logogoogle play logo