What is the integral of x^9sin(x^{10}) ?

The integral of x^9sin(x^{10}) is -1/10 cos(x^{10})+C

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integral of x^9sin(x^{10})

\int x^{9} sin (x^{10}) d x

- \frac{1}{10} cos (x^{10}) + C

Solution steps

\int x^{9} sin (x^{10}) d x

Apply u-substitution

= \int \frac{sin ( u )}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{10} (- cos (u))

Substitute back

u = x^{10}

= \frac{1}{10} (- cos (x^{10}))

Simplify

= - \frac{1}{10} cos (x^{10})

Add a constant to the solution

= - \frac{1}{10} cos (x^{10}) + C

What is the integral of x^9sin(x^{10}) ?
The integral of x^9sin(x^{10}) is -1/10 cos(x^{10})+C