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

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

Popular >

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

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

- 5 sin (cos (x)) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int - cos (u) d u

= 5 \cdot \int - cos (u) d u

Take the constant out:

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

= 5 (- \int cos (u) d u)

Use the common integral:

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

= 5 (- sin (u))

Substitute back

u = cos (x)

= 5 (- sin (cos (x)))

Simplify

= - 5 sin (cos (x))

Add a constant to the solution

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

\int e^{2 x - 5} d x

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

\int \frac{x ^{2}}{x ^{4}} d x

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

\int \frac{- 3}{4 + x ^{2}} d x

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