What is the integral of x^4ln(2x) ?

The integral of x^4ln(2x) is 1/5 x^5ln(2x)-(x^5)/(25)+C

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integral of x^4ln(2x)

\int x^{4} ln (2 x) d x

\frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25} + C

Solution steps

\int x^{4} ln (2 x) d x

Apply Integration By Parts

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

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

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

= \frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25}

Add a constant to the solution

= \frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25} + C

\frac{d}{d x} (x^{2 a x})

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\int \frac{( 6 x ^{2} + 5 x + 6 )}{( x ^{2} + 1 ) ^{2}} d x

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What is the integral of x^4ln(2x) ?
The integral of x^4ln(2x) is 1/5 x^5ln(2x)-(x^5)/(25)+C