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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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Rewrite the integrand $x\left(\ln\left(1+x^2\right)+e^{-x}\right)$ in expanded form
Learn how to solve integration by parts problems step by step online.
$\int\left(x\ln\left(1+x^2\right)+e^{-x}x\right)dx$
Learn how to solve integration by parts problems step by step online. Solve the integral of logarithmic functions int(x(ln(1+x^2)+e^(-x)))dx. Rewrite the integrand x\left(\ln\left(1+x^2\right)+e^{-x}\right) in expanded form. Expand the integral \int\left(x\ln\left(1+x^2\right)+e^{-x}x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Multiply the single term \frac{1}{2} by each term of the polynomial \left(\ln\left(1+x^2\right)+x^2\ln\left(1+x^2\right)-1-x^2\right). The integral \int x\ln\left(1+x^2\right)dx results in: \frac{1}{2}\ln\left(1+x^2\right)+\frac{1}{2}x^2\ln\left(1+x^2\right)-\frac{1}{2}-\frac{1}{2}x^2.
