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

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

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

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

cos (cos (x)) + C

Solution steps

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

Apply u-substitution

: \int - sin (u) d u

= \int - sin (u) d u

Take the constant out:

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

= - \int sin (u) d u

Use the common integral:

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

= - (- cos (u))

Substitute back

u = cos (x)

= - (- cos (cos (x)))

Simplify

= cos (cos (x))

Add a constant to the solution

= cos (cos (x)) + C

\frac{\partial}{\partial u} (u v^{2})

\frac{d}{d x} (\frac{7}{x - 3})

- 3 cos (3 x)

f (x) = \frac{x ^{2}}{x ^{3} + 1}

\int_{2}^{7} \frac{1}{x - 2} d x

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