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

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

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

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

- sin (cos (x)) + C

Solution steps

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

Apply u-substitution

: \int - cos (u) d u

= \int - cos (u) d u

Take the constant out:

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

= - \int cos (u) d u

Use the common integral:

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

= - sin (u)

Substitute back

u = cos (x)

= - sin (cos (x))

Add a constant to the solution

= - sin (cos (x)) + C

\int_{1}^{x^{2}} \frac{1}{t} d t

\int (\frac{x ^{4} - 3 x ^{2} + 5}{x ^{4}}) d x

x^{2} \frac{d y}{d x} - x = 1 + y + x y

f (x) = 12 x

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

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