Math  /  Math Statement

QuestionEvaluate the integral: x3(4+x2)32dx\int x^{3}\left(4+x^{2}\right)^{\frac{3}{2}} d x

Studdy Solution
Substitute uu back into the equation to get the final result.
2[25u52163u32]+C=2[25(4+x2)52163(4+x2)32]+C\frac{}{2} \left[ \frac{2}{5} u^{\frac{5}{2}} - \frac{16}{3} u^{\frac{3}{2}} \right] + C = \frac{}{2} \left[ \frac{2}{5} (4+x^{2})^{\frac{5}{2}} - \frac{16}{3} (4+x^{2})^{\frac{3}{2}} \right] + CSo, the integral x3(4+x2)32dx\int x^{3}\left(4+x^{2}\right)^{\frac{3}{2}} dx equals to 2[25(4+x2)52163(4+x2)32]+C\frac{}{2} \left[ \frac{2}{5} (4+x^{2})^{\frac{5}{2}} - \frac{16}{3} (4+x^{2})^{\frac{3}{2}} \right] + C.

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