$\int \frac{x^{2}+2}{\sqrt{x}} d x=\frac{2}{5} x^{\frac{5}{2}}+4 x^{\frac{1}{2}}+C$ .

Name: $\int \frac{x^{2}+2}{\sqrt{x}} d x=\frac{2}{5} x^{\frac{5}{2}}+4 x^{\frac{1}{2}}+C$ .
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Question

Quizplus · Accepted Answer

To solve the integral $\int \frac{x^{2}+2}{\sqrt{x}} dx$, rewrite it as $\int x^{\frac{3}{2}} + 2x^{-\frac{1}{2}} dx$. Integrating term by term gives $\frac{2}{5}x^{\frac{5}{2}} + 4x^{\frac{1}{2}} + C$, which matches the given expression.

∫x2+2xdx=25x52+4x12+C\int \frac{x^{2}+2}{\sqrt{x}} d x=\frac{2}{5} x^{\frac{5}{2}}+4 x^{\frac{1}{2}}+C∫x​x2+2​dx=52​x25​+4x21​+C

$\int \frac{x^{2}+2}{\sqrt{x}} d x=\frac{2}{5} x^{\frac{5}{2}}+4 x^{\frac{1}{2}}+C$