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

The integral of cos(x)cos(5sin(x)) is 1/5 sin(5sin(x))+C

Popular >

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

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

\frac{1}{5} sin (5 sin (x)) + C

Solution steps

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

Apply u-substitution

: \int cos (5 u) d u

= \int cos (5 u) d u

Apply u-substitution

: \int cos (v) \frac{1}{5} d v

= \int cos (v) \frac{1}{5} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int cos (v) d v

Use the common integral:

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

= \frac{1}{5} sin (v)

Substitute back

= \frac{1}{5} sin (5 sin (x))

Add a constant to the solution

= \frac{1}{5} sin (5 sin (x)) + C

\int sec (2) (x) tan (2) (x) d x

\int 1 - \frac{1}{x ^{2}} \frac{1}{x ^{3}} d x

\int \frac{2 z - 3}{z ^{2} - 6 z + 13} d z

\int p (p + 4)^{4} d p

\int (e^{6 x} + 6) (e^{- 2 x} + 12) d x

What is the integral of cos(x)cos(5sin(x)) ?
The integral of cos(x)cos(5sin(x)) is 1/5 sin(5sin(x))+C