What is the integral of sin(x/(10))cos^4(x/(10)) ?

The integral of sin(x/(10))cos^4(x/(10)) is -2cos^5(x/(10))+C

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integral of sin(x/(10))cos^4(x/(10))

\int sin (\frac{x}{10}) cos^{4} (\frac{x}{10}) d x

- 2 cos^{5} (\frac{x}{10}) + C

Solution steps

\int sin (\frac{x}{10}) cos^{4} (\frac{x}{10}) d x

Apply u-substitution

: \int sin (u) cos^{4} (u) \cdot 10 d u

= \int sin (u) cos^{4} (u) \cdot 10 d u

Take the constant out:

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

= 10 \cdot \int sin (u) cos^{4} (u) d u

Apply u-substitution

: \int - v^{4} d v

= 10 \cdot \int - v^{4} d v

Take the constant out:

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

= 10 (- \int v^{4} d v)

Apply the Power Rule

: \frac{v ^{5}}{5}

= 10 (- \frac{v ^{5}}{5})

Substitute back

= 10 (- \frac{cos ^{5} ( \frac{x}{10} )}{5})

Simplify

10 (- \frac{cos ^{5} ( \frac{x}{10} )}{5}) : - 2 cos^{5} (\frac{x}{10})

= - 2 cos^{5} (\frac{x}{10})

Add a constant to the solution

= - 2 cos^{5} (\frac{x}{10}) + C

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What is the integral of sin(x/(10))cos^4(x/(10)) ?
The integral of sin(x/(10))cos^4(x/(10)) is -2cos^5(x/(10))+C