What is the integral of 4xln(8x^3) ?

The integral of 4xln(8x^3) is 6x^2ln(2x)-3x^2+C

Popular >

integral of 4xln(8x^3)

\int 4 x ln (8 x^{3}) d x

6 x^{2} ln (2 x) - 3 x^{2} + C

Solution steps

\int 4 x ln (8 x^{3}) d x

Take the constant out:

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

= 4 \cdot \int x ln (8 x^{3}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (8 x^{3}) - \int \frac{3 x}{2} d x

= 4 (\frac{1}{2} x^{2} ln (8 x^{3}) - \int \frac{3 x}{2} d x)

\int \frac{3 x}{2} d x = \frac{3 x ^{2}}{4}

= 4 (\frac{1}{2} x^{2} ln (8 x^{3}) - \frac{3 x ^{2}}{4})

Simplify

4 (\frac{1}{2} x^{2} ln (8 x^{3}) - \frac{3 x ^{2}}{4}) : 6 x^{2} ln (2 x) - 3 x^{2}

= 6 x^{2} ln (2 x) - 3 x^{2}

Add a constant to the solution

= 6 x^{2} ln (2 x) - 3 x^{2} + C

\int (7 - 2 x)^{12} d x

\int \frac{x + 1}{x ^{2} + 10 x + 34} d x

\int \frac{- cos ( 3 x )}{1 - sin ( 3 x )} d x

\int \frac{1}{cos ^{2} ( x ) + 4 sin ^{2} ( x )} d x

\int - \frac{1}{4 x ^{2}} d x

What is the integral of 4xln(8x^3) ?
The integral of 4xln(8x^3) is 6x^2ln(2x)-3x^2+C