What is the integral of x(3x+5)^{11} ?

The integral of x(3x+5)^{11} is 1/36 x(3x+5)^{12}-1/1404 (3x+5)^{13}+C

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integral of x(3x+5)^{11}

\int x (3 x + 5)^{11} d x

\frac{1}{36} x (3 x + 5)^{12} - \frac{1}{1404} (3 x + 5)^{13} + C

Solution steps

\int x (3 x + 5)^{11} d x

Apply Integration By Parts

= \frac{1}{36} x (3 x + 5)^{12} - \int \frac{1}{36} (3 x + 5)^{12} d x

\int \frac{1}{36} (3 x + 5)^{12} d x = \frac{1}{1404} (3 x + 5)^{13}

= \frac{1}{36} x (3 x + 5)^{12} - \frac{1}{1404} (3 x + 5)^{13}

Add a constant to the solution

= \frac{1}{36} x (3 x + 5)^{12} - \frac{1}{1404} (3 x + 5)^{13} + C

What is the integral of x(3x+5)^{11} ?
The integral of x(3x+5)^{11} is 1/36 x(3x+5)^{12}-1/1404 (3x+5)^{13}+C