What is the integral of x(3x-5)^{10} ?

The integral of x(3x-5)^{10} is 1/33 x(3x-5)^{11}-1/1188 (3x-5)^{12}+C

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integral of x(3x-5)^{10}

\int x (3 x - 5)^{10} d x

\frac{1}{33} x (3 x - 5)^{11} - \frac{1}{1188} (3 x - 5)^{12} + C

Solution steps

\int x (3 x - 5)^{10} d x

Apply Integration By Parts

: \frac{1}{33} x (3 x - 5)^{11} - \int \frac{1}{33} (3 x - 5)^{11} d x

= \frac{1}{33} x (3 x - 5)^{11} - \int \frac{1}{33} (3 x - 5)^{11} d x

\int \frac{1}{33} (3 x - 5)^{11} d x = \frac{1}{1188} (3 x - 5)^{12}

= \frac{1}{33} x (3 x - 5)^{11} - \frac{1}{1188} (3 x - 5)^{12}

Add a constant to the solution

= \frac{1}{33} x (3 x - 5)^{11} - \frac{1}{1188} (3 x - 5)^{12} + C

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What is the integral of x(3x-5)^{10} ?
The integral of x(3x-5)^{10} is 1/33 x(3x-5)^{11}-1/1188 (3x-5)^{12}+C