What is the integral of sqrt(x)(2x+7) ?

The integral of sqrt(x)(2x+7) is 2/3 x^{3/2}(2x+7)-8/15 x^{5/2}+C

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integral of sqrt(x)(2x+7)

\int x (2 x + 7) d x

\frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \frac{8}{15} x^{\frac{5}{2}} + C

Solution steps

\int x (2 x + 7) d x

Apply Integration By Parts

: \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \int \frac{4}{3} x^{\frac{3}{2}} d x

= \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \int \frac{4}{3} x^{\frac{3}{2}} d x

\int \frac{4}{3} x^{\frac{3}{2}} d x = \frac{8}{15} x^{\frac{5}{2}}

= \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \frac{8}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \frac{8}{15} x^{\frac{5}{2}} + C

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What is the integral of sqrt(x)(2x+7) ?
The integral of sqrt(x)(2x+7) is 2/3 x^{3/2}(2x+7)-8/15 x^{5/2}+C