What is the integral of x^{19}sin(x^{20}) ?

The integral of x^{19}sin(x^{20}) is -1/20 cos(x^{20})+C

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integral of x^{19}sin(x^{20})

\int x^{19} sin (x^{20}) d x

- \frac{1}{20} cos (x^{20}) + C

Solution steps

\int x^{19} sin (x^{20}) d x

Apply u-substitution

: \int \frac{sin ( u )}{20} d u

= \int \frac{sin ( u )}{20} d u

Take the constant out:

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

= \frac{1}{20} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{20} (- cos (u))

Substitute back

u = x^{20}

= \frac{1}{20} (- cos (x^{20}))

Simplify

= - \frac{1}{20} cos (x^{20})

Add a constant to the solution

= - \frac{1}{20} cos (x^{20}) + C

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What is the integral of x^{19}sin(x^{20}) ?
The integral of x^{19}sin(x^{20}) is -1/20 cos(x^{20})+C