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Popular >

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

Solution

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

Solution

- \frac{1}{9} cos (e^{9 x}) + C

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{9} d u

= \int \frac{sin ( u )}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{9} (- cos (u))

Substitute back

u = e^{9 x}

= \frac{1}{9} (- cos (e^{9 x}))

Simplify

= - \frac{1}{9} cos (e^{9 x})

Add a constant to the solution

= - \frac{1}{9} cos (e^{9 x}) + C

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\int sec^{2} (4 x) tan^{2} (4 x) d x

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\int \frac{1}{x ^{3} x} d x

Frequently Asked Questions (FAQ)

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