Menu buton
qanda-logo
apple logogoogle play logo

Hasil perhitungan rumus

Rumus
Hitunglah integralnya
Jawaban
circle-check-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
$$\displaystyle\int { \dfrac { 1 } { \cos\left( x \right) } } d { x }$$
$- 1 \left ( \dfrac { 1 } { 2 } \ln { \left( | \sin\left( x \right) - 1 | \right) } - \dfrac { 1 } { 2 } \ln { \left( | \sin\left( x \right) + 1 | \right) } \right )$
Hitunglah integralnya
$\displaystyle\int { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ \cos\left( \color{#FF6800}{ x } \right) } } } } d { \color{#FF6800}{ x } }$
$ $ Substitusikanlah menjadi $ u = \sin\left( x \right) $ dan hitunglah integralnya. $ $
$\left [ \displaystyle\int { \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } } } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } }$
$\left [ \displaystyle\int { \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } } } } d { \color{#FF6800}{ u } } \right ] _ { u = \sin\left( x \right) }$
$ $ Buatlah koefisien dari suku tertinggi pada penyebut menjadi 1. $ $
$\left [ \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } \displaystyle\int { \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } } d { \color{#FF6800}{ u } } \right ] _ { u = \sin\left( x \right) }$
$\left [ \frac { 1 } { - 1 } \displaystyle\int { \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } } d { \color{#FF6800}{ u } } \right ] _ { u = \sin\left( x \right) }$
$ $ Hitunglah integralnya menggunakan integral parsial $ $
$\left [ \frac { 1 } { - 1 } \left ( \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \left [ \displaystyle\int { \color{#FF6800}{ v } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } d { \color{#FF6800}{ v } } \right ] _ { \color{#FF6800}{ v } = \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \color{#FF6800}{ - } \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \left [ \displaystyle\int { \color{#FF6800}{ v } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } d { \color{#FF6800}{ v } } \right ] _ { \color{#FF6800}{ v } = \color{#FF6800}{ u } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ) \right ] _ { u = \sin\left( x \right) }$
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \left [ \displaystyle\int { \color{#FF6800}{ v } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } d { \color{#FF6800}{ v } } \right ] _ { v = u - 1 } - \frac { 1 } { 2 } \left [ \displaystyle\int { v ^ { - 1 } } d { v } \right ] _ { v = u + 1 } \right ) \right ] _ { u = \sin\left( x \right) }$
$ $ Gunakanlah rumus $ \int x^{-1} dx = \ln(|x|) $ dan hitunglah integralnya. $ $
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \left [ \ln { \left( | \color{#FF6800}{ v } | \right) } \right ] _ { v = u - 1 } - \frac { 1 } { 2 } \left [ \displaystyle\int { v ^ { - 1 } } d { v } \right ] _ { v = u + 1 } \right ) \right ] _ { u = \sin\left( x \right) }$
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \left [ \ln { \left( | \color{#FF6800}{ v } | \right) } \right ] _ { \color{#FF6800}{ v } = \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } - \frac { 1 } { 2 } \left [ \displaystyle\int { v ^ { - 1 } } d { v } \right ] _ { v = u + 1 } \right ) \right ] _ { u = \sin\left( x \right) }$
$ $ Kembalikanlah nilai yang telah disubstitusi. $ $
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \ln { \left( | \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 1 } | \right) } - \frac { 1 } { 2 } \left [ \displaystyle\int { v ^ { - 1 } } d { v } \right ] _ { v = u + 1 } \right ) \right ] _ { u = \sin\left( x \right) }$
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \ln { \left( | u - 1 | \right) } - \frac { 1 } { 2 } \left [ \displaystyle\int { \color{#FF6800}{ v } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } d { \color{#FF6800}{ v } } \right ] _ { v = u + 1 } \right ) \right ] _ { u = \sin\left( x \right) }$
$ $ Gunakanlah rumus $ \int x^{-1} dx = \ln(|x|) $ dan hitunglah integralnya. $ $
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \ln { \left( | u - 1 | \right) } - \frac { 1 } { 2 } \left [ \ln { \left( | \color{#FF6800}{ v } | \right) } \right ] _ { v = u + 1 } \right ) \right ] _ { u = \sin\left( x \right) }$
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \ln { \left( | u - 1 | \right) } - \frac { 1 } { 2 } \left [ \ln { \left( | \color{#FF6800}{ v } | \right) } \right ] _ { \color{#FF6800}{ v } = \color{#FF6800}{ u } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ) \right ] _ { u = \sin\left( x \right) }$
$ $ Kembalikanlah nilai yang telah disubstitusi. $ $
$\left [ \frac { 1 } { - 1 } \left ( \frac { 1 } { 2 } \ln { \left( | u - 1 | \right) } - \frac { 1 } { 2 } \ln { \left( | \color{#FF6800}{ u } \color{#FF6800}{ + } \color{#FF6800}{ 1 } | \right) } \right ) \right ] _ { u = \sin\left( x \right) }$
$\left [ \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } \left ( \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \ln { \left( | \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 1 } | \right) } \color{#FF6800}{ - } \color{#FF6800}{ \frac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \ln { \left( | \color{#FF6800}{ u } \color{#FF6800}{ + } \color{#FF6800}{ 1 } | \right) } \right ) \right ] _ { \color{#FF6800}{ u } = \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } }$
$ $ Kembalikanlah nilai yang telah disubstitusi. $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \ln { \left( | \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \color{#FF6800}{ 1 } | \right) } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \ln { \left( | \color{#FF6800}{ \sin\left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ + } \color{#FF6800}{ 1 } | \right) } \right )$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } \left ( \dfrac { 1 } { 2 } \ln { \left( | \sin\left( x \right) - 1 | \right) } - \dfrac { 1 } { 2 } \ln { \left( | \sin\left( x \right) + 1 | \right) } \right )$
$ $ Hitung nilainya $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \left ( \dfrac { 1 } { 2 } \ln { \left( | \sin\left( x \right) - 1 | \right) } - \dfrac { 1 } { 2 } \ln { \left( | \sin\left( x \right) + 1 | \right) } \right )$
Coba lebih banyak fitur lain dengan app Qanda!
Cari dengan memfoto soalnya
Bertanya 1:1 ke guru TOP
Rekomendasi soal & konsep pembelajaran oleh AI
apple logogoogle play logo