What is the integral of x^5ln(4x^3) ?

The integral of x^5ln(4x^3) is 1/6 x^6(2ln(2)+3ln(x))-(x^6)/(12)+C

Popular >

integral of x^5ln(4x^3)

\int x^{5} ln (4 x^{3}) d x

\frac{1}{6} x^{6} (2 ln (2) + 3 ln (x)) - \frac{x ^{6}}{12} + C

Solution steps

\int x^{5} ln (4 x^{3}) d x

Apply Integration By Parts

: \frac{1}{6} x^{6} ln (4 x^{3}) - \int \frac{x ^{5}}{2} d x

= \frac{1}{6} x^{6} ln (4 x^{3}) - \int \frac{x ^{5}}{2} d x

\int \frac{x ^{5}}{2} d x = \frac{x ^{6}}{12}

= \frac{1}{6} x^{6} ln (4 x^{3}) - \frac{x ^{6}}{12}

\frac{1}{6} x^{6} ln (4 x^{3}) = \frac{1}{6} x^{6} (2 ln (2) + 3 ln (x))

= \frac{1}{6} x^{6} (2 ln (2) + 3 ln (x)) - \frac{x ^{6}}{12}

Add a constant to the solution

= \frac{1}{6} x^{6} (2 ln (2) + 3 ln (x)) - \frac{x ^{6}}{12} + C

\int 5 x + 4 d x

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

\int 1 - e^{2 x} d x

\int 12 sec^{2} (x) tan^{3} (x) d x

\int \frac{10000 x}{x ^{2} + e} d x

What is the integral of x^5ln(4x^3) ?
The integral of x^5ln(4x^3) is 1/6 x^6(2ln(2)+3ln(x))-(x^6)/(12)+C