What is the integral of x(3x+1)^7 ?

The integral of x(3x+1)^7 is 1/24 x(3x+1)^8-1/648 (3x+1)^9+C

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integral of x(3x+1)^7

\int x (3 x + 1)^{7} d x

\frac{1}{24} x (3 x + 1)^{8} - \frac{1}{648} (3 x + 1)^{9} + C

Solution steps

\int x (3 x + 1)^{7} d x

Apply Integration By Parts

: \frac{1}{24} x (3 x + 1)^{8} - \int \frac{1}{24} (3 x + 1)^{8} d x

= \frac{1}{24} x (3 x + 1)^{8} - \int \frac{1}{24} (3 x + 1)^{8} d x

\int \frac{1}{24} (3 x + 1)^{8} d x = \frac{1}{648} (3 x + 1)^{9}

= \frac{1}{24} x (3 x + 1)^{8} - \frac{1}{648} (3 x + 1)^{9}

Add a constant to the solution

= \frac{1}{24} x (3 x + 1)^{8} - \frac{1}{648} (3 x + 1)^{9} + C

(t + 5)^{3}

\frac{d}{d x} (\frac{ln ( x )}{x ^{13}})

\frac{10}{x}

x \to a lim (\frac{x - 1}{3 x + 6})

\int (x ln (x)) d x

What is the integral of x(3x+1)^7 ?
The integral of x(3x+1)^7 is 1/24 x(3x+1)^8-1/648 (3x+1)^9+C