What is the integral of \sqrt[6]{x}ln(x) ?

The integral of \sqrt[6]{x}ln(x) is 6/7 x^{7/6}ln(x)-36/49 x^{7/6}+C

Popular >

integral of \sqrt[6]{x}ln(x)

\frac{6}{7} x^{\frac{7}{6}} ln (x) - \frac{36}{49} x^{\frac{7}{6}} + C

Solution steps

Apply Integration By Parts

: \frac{6}{7} x^{\frac{7}{6}} ln (x) - \int \frac{6}{7} x^{\frac{1}{6}} d x

= \frac{6}{7} x^{\frac{7}{6}} ln (x) - \int \frac{6}{7} x^{\frac{1}{6}} d x

\int \frac{6}{7} x^{\frac{1}{6}} d x = \frac{36}{49} x^{\frac{7}{6}}

= \frac{6}{7} x^{\frac{7}{6}} ln (x) - \frac{36}{49} x^{\frac{7}{6}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{6}} ln (x) - \frac{36}{49} x^{\frac{7}{6}} + C

\int \frac{cot ( x )}{cos ^{2} ( x )} d x

\int (1 + cot (x))^{4} (csc (x))^{2} d x

\int \frac{3 x ^{2} + 9 x + 1}{x} d x

\int \frac{sec ^{2} ( z )}{3 + 5 tan ( z )} d z

\int \frac{cos ( x )}{4} d x

What is the integral of \sqrt[6]{x}ln(x) ?
The integral of \sqrt[6]{x}ln(x) is 6/7 x^{7/6}ln(x)-36/49 x^{7/6}+C