What is the integral of x(3x+8)^5 ?

The integral of x(3x+8)^5 is 1/18 x(3x+8)^6-1/378 (3x+8)^7+C

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integral of x(3x+8)^5

\int x (3 x + 8)^{5} d x

\frac{1}{18} x (3 x + 8)^{6} - \frac{1}{378} (3 x + 8)^{7} + C

Solution steps

\int x (3 x + 8)^{5} d x

Apply Integration By Parts

= \frac{1}{18} x (3 x + 8)^{6} - \int \frac{1}{18} (3 x + 8)^{6} d x

\int \frac{1}{18} (3 x + 8)^{6} d x = \frac{1}{378} (3 x + 8)^{7}

= \frac{1}{18} x (3 x + 8)^{6} - \frac{1}{378} (3 x + 8)^{7}

Add a constant to the solution

= \frac{1}{18} x (3 x + 8)^{6} - \frac{1}{378} (3 x + 8)^{7} + C

What is the integral of x(3x+8)^5 ?
The integral of x(3x+8)^5 is 1/18 x(3x+8)^6-1/378 (3x+8)^7+C