What is the integral of x^{27}sin(x^{28}) ?

The integral of x^{27}sin(x^{28}) is -1/28 cos(x^{28})+C

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integral of x^{27}sin(x^{28})

\int x^{27} sin (x^{28}) d x

- \frac{1}{28} cos (x^{28}) + C

Solution steps

\int x^{27} sin (x^{28}) d x

Apply u-substitution

: \int \frac{sin ( u )}{28} d u

= \int \frac{sin ( u )}{28} d u

Take the constant out:

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

= \frac{1}{28} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{28} (- cos (u))

Substitute back

u = x^{28}

= \frac{1}{28} (- cos (x^{28}))

Simplify

= - \frac{1}{28} cos (x^{28})

Add a constant to the solution

= - \frac{1}{28} cos (x^{28}) + C

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What is the integral of x^{27}sin(x^{28}) ?
The integral of x^{27}sin(x^{28}) is -1/28 cos(x^{28})+C