What is the integral of 2x(3x-5)^{10} ?

The integral of 2x(3x-5)^{10} is 2(1/33 x(3x-5)^{11}-1/1188 (3x-5)^{12})+C

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integral of 2x(3x-5)^{10}

\int 2 x (3 x - 5)^{10} d x

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

Solution steps

\int 2 x (3 x - 5)^{10} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \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

= 2 (\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}

= 2 (\frac{1}{33} x (3 x - 5)^{11} - \frac{1}{1188} (3 x - 5)^{12})

Add a constant to the solution

= 2 (\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 2x(3x-5)^{10} ?
The integral of 2x(3x-5)^{10} is 2(1/33 x(3x-5)^{11}-1/1188 (3x-5)^{12})+C