Final answer to the problem
$\frac{4\sqrt{x^{3}}}{3}+\frac{2\sqrt{x^{5}}}{5}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Rewrite the integrand $\sqrt{x}\left(2+x\right)$ in expanded form
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$\int\left(2\sqrt{x}+\sqrt{x^{3}}\right)dx$
Learn how to solve problems step by step online. Integrate int(x^(1/2)(2+x))dx. Rewrite the integrand \sqrt{x}\left(2+x\right) in expanded form. Expand the integral \int\left(2\sqrt{x}+\sqrt{x^{3}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2\sqrt{x}dx results in: \frac{4\sqrt{x^{3}}}{3}. The integral \int\sqrt{x^{3}}dx results in: \frac{2\sqrt{x^{5}}}{5}.
Final answer to the problem
$\frac{4\sqrt{x^{3}}}{3}+\frac{2\sqrt{x^{5}}}{5}+C_0$
