What is the integral of sqrt(x)(x^2-5) ?

The integral of sqrt(x)(x^2-5) is 2/3 x^{3/2}(x^2-5)-8/21 x^{7/2}+C

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integral of sqrt(x)(x^2-5)

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

\frac{2}{3} x^{\frac{3}{2}} (x^{2} - 5) - \frac{8}{21} x^{\frac{7}{2}} + C

Solution steps

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

Apply Integration By Parts

: \frac{2}{3} x^{\frac{3}{2}} (x^{2} - 5) - \int \frac{4}{3} x^{\frac{5}{2}} d x

= \frac{2}{3} x^{\frac{3}{2}} (x^{2} - 5) - \int \frac{4}{3} x^{\frac{5}{2}} d x

\int \frac{4}{3} x^{\frac{5}{2}} d x = \frac{8}{21} x^{\frac{7}{2}}

= \frac{2}{3} x^{\frac{3}{2}} (x^{2} - 5) - \frac{8}{21} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} (x^{2} - 5) - \frac{8}{21} x^{\frac{7}{2}} + C

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What is the integral of sqrt(x)(x^2-5) ?
The integral of sqrt(x)(x^2-5) is 2/3 x^{3/2}(x^2-5)-8/21 x^{7/2}+C