What is the integral of x(4x-3)^{10} ?

The integral of x(4x-3)^{10} is 1/44 x(4x-3)^{11}-1/2112 (4x-3)^{12}+C

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integral of x(4x-3)^{10}

\int x (4 x - 3)^{10} d x

\frac{1}{44} x (4 x - 3)^{11} - \frac{1}{2112} (4 x - 3)^{12} + C

Solution steps

\int x (4 x - 3)^{10} d x

Apply Integration By Parts

= \frac{1}{44} x (4 x - 3)^{11} - \int \frac{1}{44} (4 x - 3)^{11} d x

\int \frac{1}{44} (4 x - 3)^{11} d x = \frac{1}{2112} (4 x - 3)^{12}

= \frac{1}{44} x (4 x - 3)^{11} - \frac{1}{2112} (4 x - 3)^{12}

Add a constant to the solution

= \frac{1}{44} x (4 x - 3)^{11} - \frac{1}{2112} (4 x - 3)^{12} + C

What is the integral of x(4x-3)^{10} ?
The integral of x(4x-3)^{10} is 1/44 x(4x-3)^{11}-1/2112 (4x-3)^{12}+C