What is the integral of 8^xsin(8^x) ?

The integral of 8^xsin(8^x) is -1/(3ln(2))cos(8^x)+C

Popular >

integral of 8^xsin(8^x)

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

- \frac{1}{3 ln ( 2 )} cos (8^{x}) + C

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{3 ln ( 2 )} d u

= \int \frac{sin ( u )}{3 ln ( 2 )} d u

Take the constant out:

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

= \frac{1}{3 ln ( 2 )} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{3 ln ( 2 )} (- cos (u))

Substitute back

u = 8^{x}

= \frac{1}{3 ln ( 2 )} (- cos (8^{x}))

Simplify

= - \frac{1}{3 ln ( 2 )} cos (8^{x})

Add a constant to the solution

= - \frac{1}{3 ln ( 2 )} cos (8^{x}) + C

\int (2 x) (1 - x^{- 3}) d x

\int \frac{cos ( x )}{2 sin ( x ) + 3} d x

\int \frac{1 + 2 x}{2 - 3 x} d x

\int \frac{6}{( x - 8 ) ( x - 2 )} d x

What is the integral of 8^xsin(8^x) ?
The integral of 8^xsin(8^x) is -1/(3ln(2))cos(8^x)+C