Question: "Evaluate the integral. ∫x(x3+x2)dx"

Tahmid Knox

Answered question

2020-10-21

Evaluate the integral.

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

bahaistag

Skilled2020-10-22Added 100 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{3}{2} + 1} + c

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

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

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

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