Solved: "Find the following integral. ∫x(x3+x2)dx"

facas9

Answered question

2021-01-13

Find the following integral.

\int \sqrt{x} (x^{3} + \frac{x}{2}) d x

Raheem Donnelly

Skilled2021-01-14Added 75 answers

Given that

\int \sqrt{x} (x^{3} + \frac{x}{2}) d x

= \int (x^{3 + \frac{1}{2}} + \frac{x^{\frac{1}{2} \cdot x}}{2}) d x

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

= \frac{x^{\frac{7}{2} + 1}}{\frac{7}{2} + 1} + \frac{x^{\frac{3}{2} + 1}}{\frac{\frac{3}{2} + 1}{2}} + C

= \frac{2}{9} x^{\frac{9}{2}} + \frac{1}{2} \cdot \frac{2}{5} \cdot x^{\frac{5}{2}} + C

= \frac{2}{9} x^{\frac{9}{2}} + \frac{1}{5} \cdot x^{\frac{5}{2}} + C

∴ \int \sqrt{x} (x^{3} + \frac{x}{2}) d x = \frac{2}{9} \cdot x^{\frac{9}{2}} + \frac{1}{5} \cdot x^{\frac{5}{2}} + C

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