What is the integral of \sqrt[4]{x}ln(7x) ?

The integral of \sqrt[4]{x}ln(7x) is 4/5 x^{5/4}ln(7x)-16/25 x^{5/4}+C

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integral of \sqrt[4]{x}ln(7x)

\int 4 x ln (7 x) d x

\frac{4}{5} x^{\frac{5}{4}} ln (7 x) - \frac{16}{25} x^{\frac{5}{4}} + C

Solution steps

\int 4 x ln (7 x) d x

Apply Integration By Parts

: \frac{4}{5} x^{\frac{5}{4}} ln (7 x) - \int \frac{4}{5} x^{\frac{1}{4}} d x

= \frac{4}{5} x^{\frac{5}{4}} ln (7 x) - \int \frac{4}{5} x^{\frac{1}{4}} d x

\int \frac{4}{5} x^{\frac{1}{4}} d x = \frac{16}{25} x^{\frac{5}{4}}

= \frac{4}{5} x^{\frac{5}{4}} ln (7 x) - \frac{16}{25} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{4}} ln (7 x) - \frac{16}{25} x^{\frac{5}{4}} + C

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What is the integral of \sqrt[4]{x}ln(7x) ?
The integral of \sqrt[4]{x}ln(7x) is 4/5 x^{5/4}ln(7x)-16/25 x^{5/4}+C