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

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

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

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

- 2 sin (cos (x)) + C

Solution steps

\int 2 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

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

Apply u-substitution

: \int - cos (u) d u

= 2 \cdot \int - cos (u) d u

Take the constant out:

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

= 2 (- \int cos (u) d u)

Use the common integral:

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

= 2 (- sin (u))

Substitute back

u = cos (x)

= 2 (- sin (cos (x)))

Simplify

= - 2 sin (cos (x))

Add a constant to the solution

= - 2 sin (cos (x)) + C

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

x \to n - lim (f (x))

\int_{0}^{π} 5 sin (x) d x

x \to 1 lim (\frac{x ^{2} - 4}{x - 2})

4 (5 - 9 x)^{5}

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