What is the integral of x(5+2x)^4 ?

The integral of x(5+2x)^4 is 1/10 x(5+2x)^5-1/120 (5+2x)^6+C

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integral of x(5+2x)^4

\int x (5 + 2 x)^{4} d x

\frac{1}{10} x (5 + 2 x)^{5} - \frac{1}{120} (5 + 2 x)^{6} + C

Solution steps

\int x (5 + 2 x)^{4} d x

Apply Integration By Parts

: \frac{1}{10} x (5 + 2 x)^{5} - \int \frac{1}{10} (5 + 2 x)^{5} d x

= \frac{1}{10} x (5 + 2 x)^{5} - \int \frac{1}{10} (5 + 2 x)^{5} d x

\int \frac{1}{10} (5 + 2 x)^{5} d x = \frac{1}{120} (5 + 2 x)^{6}

= \frac{1}{10} x (5 + 2 x)^{5} - \frac{1}{120} (5 + 2 x)^{6}

Add a constant to the solution

= \frac{1}{10} x (5 + 2 x)^{5} - \frac{1}{120} (5 + 2 x)^{6} + C

\int (sec (2 x))^{2} d x

2 tan (x)

\int \frac{1}{2 x} d x

e^{x + 2}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 9} d x

What is the integral of x(5+2x)^4 ?
The integral of x(5+2x)^4 is 1/10 x(5+2x)^5-1/120 (5+2x)^6+C