What is the integral of x^3ln(9x^2) ?

The integral of x^3ln(9x^2) is 1/2 x^4ln(3x)-(x^4)/8+C

Popular >

integral of x^3ln(9x^2)

\int x^{3} ln (9 x^{2}) d x

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

Solution steps

\int x^{3} ln (9 x^{2}) d x

Apply Integration By Parts

: \frac{1}{4} x^{4} ln (9 x^{2}) - \int \frac{x ^{3}}{2} d x

= \frac{1}{4} x^{4} ln (9 x^{2}) - \int \frac{x ^{3}}{2} d x

\int \frac{x ^{3}}{2} d x = \frac{x ^{4}}{8}

= \frac{1}{4} x^{4} ln (9 x^{2}) - \frac{x ^{4}}{8}

\frac{1}{4} x^{4} ln (9 x^{2}) = \frac{1}{2} x^{4} ln (3 x)

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

Add a constant to the solution

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

\int \frac{1}{x \cdot ln ( x ) \cdot ln ( ln ( x ) )} d x

\int (4 sin (x) + 2 csc^{2} (x) + 4) d x

\int 1 - 4 x d x

\int \frac{50 x + 10 x ^{3}}{10 x ^{2} + x ^{4}} d x

\int sin^{2} (10 x) cos^{3} (10 x) d x

What is the integral of x^3ln(9x^2) ?
The integral of x^3ln(9x^2) is 1/2 x^4ln(3x)-(x^4)/8+C