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

The integral of x^3ln(x^3) is 3/4 x^4ln(x)-(3x^4)/(16)+C

Popular >

integral of x^3ln(x^3)

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

\frac{3}{4} x^{4} ln (x) - \frac{3 x ^{4}}{16} + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{3 x ^{3}}{4} d x = \frac{3 x ^{4}}{16}

= \frac{1}{4} x^{4} ln (x^{3}) - \frac{3 x ^{4}}{16}

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

= \frac{3}{4} x^{4} ln (x) - \frac{3 x ^{4}}{16}

Add a constant to the solution

= \frac{3}{4} x^{4} ln (x) - \frac{3 x ^{4}}{16} + C

y^{^{'}} = \frac{1}{sec ^{2} ( y )}

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 3 x )})

x \to 2 lim (e^{2 x - x^{2}})

\int y e^{z} d z

\int \frac{x ^{4} + 1}{x ^{3}} d x

What is the integral of x^3ln(x^3) ?
The integral of x^3ln(x^3) is 3/4 x^4ln(x)-(3x^4)/(16)+C