What is the integral of cos(x)cos(2sin(x)) ?

The integral of cos(x)cos(2sin(x)) is 1/2 sin(2sin(x))+C

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integral of cos(x)cos(2sin(x))

\int cos (x) cos (2 sin (x)) d x

\frac{1}{2} sin (2 sin (x)) + C

Solution steps

\int cos (x) cos (2 sin (x)) d x

Apply u-substitution

= \int \frac{cos ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = 2 sin (x)

= \frac{1}{2} sin (2 sin (x))

Add a constant to the solution

= \frac{1}{2} sin (2 sin (x)) + C

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

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

\int - \frac{4}{t} d t

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

\int \frac{1}{( w ^{2} + 5 ) ^{3}} d w

What is the integral of cos(x)cos(2sin(x)) ?
The integral of cos(x)cos(2sin(x)) is 1/2 sin(2sin(x))+C