What is the integral of x^{21}sin(x^{22}) ?

The integral of x^{21}sin(x^{22}) is -1/22 cos(x^{22})+C

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integral of x^{21}sin(x^{22})

\int x^{21} sin (x^{22}) d x

- \frac{1}{22} cos (x^{22}) + C

Solution steps

\int x^{21} sin (x^{22}) d x

Apply u-substitution

: \int \frac{sin ( u )}{22} d u

= \int \frac{sin ( u )}{22} d u

Take the constant out:

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

= \frac{1}{22} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{22} (- cos (u))

Substitute back

u = x^{22}

= \frac{1}{22} (- cos (x^{22}))

Simplify

= - \frac{1}{22} cos (x^{22})

Add a constant to the solution

= - \frac{1}{22} cos (x^{22}) + C

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What is the integral of x^{21}sin(x^{22}) ?
The integral of x^{21}sin(x^{22}) is -1/22 cos(x^{22})+C