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

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

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

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

cos (cos (x)) + C

Solution steps

\int sin (x) sin (cos (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

f (x) = 5 - x^{2}, at x = - 1

\int \frac{1}{x ^{6} - x ^{3}} d x

\int (4 x^{3} + cos (x)) d x

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}

\frac{2}{u}

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