Final Answer
$\frac{x^{3}}{3}-e^{\left(u-1\right)}u\ln\left(u\right)+e^{\left(u-1\right)}\ln\left(u\right)+C_0$
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Step-by-step Solution
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1
Multiply the single term $e^x$ by each term of the polynomial $\left(x^2+1\right)$
$\int\frac{x^2e^x+e^x}{x+1}dx$
Learn how to solve logarithmic differentiation problems step by step online.
$\int\frac{x^2e^x+e^x}{x+1}dx$
Learn how to solve logarithmic differentiation problems step by step online. Find the integral int((e^x(x^2+1))/(x+1))dx. Multiply the single term e^x by each term of the polynomial \left(x^2+1\right). Expand the fraction \frac{x^2e^x+e^x}{x+1} into 2 simpler fractions with common denominator x+1. Expand the integral \int\left(\frac{x^2e^x}{x+1}+\frac{e^x}{x+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x^2e^x}{x+1}dx results in: \frac{x^{3}}{3}.
Final Answer
$\frac{x^{3}}{3}-e^{\left(u-1\right)}u\ln\left(u\right)+e^{\left(u-1\right)}\ln\left(u\right)+C_0$