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Popular >

integral of e^{8x}sin(e^{8x})

Solution

\int e^{8 x} sin (e^{8 x}) d x

Solution

- \frac{1}{8} cos (e^{8 x}) + C

Solution steps

\int e^{8 x} sin (e^{8 x}) d x

Apply u-substitution

: \int \frac{sin ( u )}{8} d u

= \int \frac{sin ( u )}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{8} (- cos (u))

Substitute back

u = e^{8 x}

= \frac{1}{8} (- cos (e^{8 x}))

Simplify

= - \frac{1}{8} cos (e^{8 x})

Add a constant to the solution

= - \frac{1}{8} cos (e^{8 x}) + C

Popular Examples

integral of (7x)/(x^4+1)

\int \frac{7 x}{x ^{4} + 1} d x

integral of (e^{3x})/(e^x-1)

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

integral of 1/(ln(x))integral

\frac{1}{ln ( x )}

integral of xln(8x)

\int x ln (8 x) d x

integral of e^{4x}sin(e^{4x})

\int e^{4 x} sin (e^{4 x}) d x

Frequently Asked Questions (FAQ)

What is the integral of e^{8x}sin(e^{8x}) ?
The integral of e^{8x}sin(e^{8x}) is -1/8 cos(e^{8x})+C