What is the integral of cos(sin(x)-5)cos(x) ?

The integral of cos(sin(x)-5)cos(x) is sin(sin(x)-5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos(sin(x)-5)cos(x)

\int cos (sin (x) - 5) cos (x) d x

sin (sin (x) - 5) + C

Solution steps

\int cos (sin (x) - 5) cos (x) d x

Apply u-substitution

= \int cos (u - 5) d u

Apply u-substitution

= \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= sin (v)

Substitute back

= sin (sin (x) - 5)

Add a constant to the solution

= sin (sin (x) - 5) + C

\int \frac{x}{x + 11} d x

\int x (x^{3} + 1) d x

\int \frac{1}{( x - 3 ) ^{4}} d x

\int \frac{3}{( x ^{2} + 5 ) ^{2}} d x

\int \frac{1}{( 1 + x ^{2} ) 1 + x ^{2}} d x

What is the integral of cos(sin(x)-5)cos(x) ?
The integral of cos(sin(x)-5)cos(x) is sin(sin(x)-5)+C