What is the integral of x^7ln(5x) ?

The integral of x^7ln(5x) is 1/8 x^8ln(5x)-(x^8)/(64)+C

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integral of x^7ln(5x)

\int x^{7} ln (5 x) d x

\frac{1}{8} x^{8} ln (5 x) - \frac{x ^{8}}{64} + C

Solution steps

\int x^{7} ln (5 x) d x

Apply Integration By Parts

: \frac{1}{8} x^{8} ln (5 x) - \int \frac{x ^{7}}{8} d x

= \frac{1}{8} x^{8} ln (5 x) - \int \frac{x ^{7}}{8} d x

\int \frac{x ^{7}}{8} d x = \frac{x ^{8}}{64}

= \frac{1}{8} x^{8} ln (5 x) - \frac{x ^{8}}{64}

Add a constant to the solution

= \frac{1}{8} x^{8} ln (5 x) - \frac{x ^{8}}{64} + C

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

\int_{- π}^{π} sin (n x) d x

e^{t} (t + 5)^{3}

\frac{\partial ^{2}}{\partial h ( w ) \partial w} (\frac{w}{h ( w ) ( w ) ^{2}})

\frac{5 e ^{- s}}{4 s ^{2} + 36}

What is the integral of x^7ln(5x) ?
The integral of x^7ln(5x) is 1/8 x^8ln(5x)-(x^8)/(64)+C