Final answer to the problem
$\frac{4\sqrt{\left(x+1\right)^{3}}}{3}+16x-2x^2+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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1
Solve the product $-\left(-16+4x\right)$
$\int\left(2\sqrt{x+1}+16-4x\right)dx$
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$\int\left(2\sqrt{x+1}+16-4x\right)dx$
Learn how to solve problems step by step online. Integrate int(2(x+1)^(1/2)-(-16+4x))dx. Solve the product -\left(-16+4x\right). Expand the integral \int\left(2\sqrt{x+1}+16-4x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2\sqrt{x+1}dx results in: \frac{4\sqrt{\left(x+1\right)^{3}}}{3}. The integral \int16dx results in: 16x.
Final answer to the problem
$\frac{4\sqrt{\left(x+1\right)^{3}}}{3}+16x-2x^2+C_0$
