Final answer to the problem
$\frac{2}{3}\left(x-\frac{5}{4}\right)^{3}-\frac{73}{8}x+C_0$
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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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- Product of Binomials with Common Term
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1
Rewrite the expression $2x^2+3x-2\left(4x+3\right)$ inside the integral in factored form
$\int\left(2\left(x-\frac{5}{4}\right)^2-\frac{73}{8}\right)dx$
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$\int\left(2\left(x-\frac{5}{4}\right)^2-\frac{73}{8}\right)dx$
Learn how to solve problems step by step online. Integrate int(2x^2+3x-2(4x+3))dx. Rewrite the expression 2x^2+3x-2\left(4x+3\right) inside the integral in factored form. Expand the integral \int\left(2\left(x-\frac{5}{4}\right)^2-\frac{73}{8}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2\left(x-\frac{5}{4}\right)^2dx results in: \frac{2}{3}\left(x-\frac{5}{4}\right)^{3}. The integral \int-\frac{73}{8}dx results in: -\frac{73}{8}x.
Final answer to the problem
$\frac{2}{3}\left(x-\frac{5}{4}\right)^{3}-\frac{73}{8}x+C_0$
