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- Integrate by partial fractions
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Simplify $e^{\left(x^2-2\ln\left|x\right|\right)}$ by applying the properties of exponents and logarithms
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$\int\left(x+\frac{-1}{x}\right)x^{-2}e^{\left(x^2\right)}dx$
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int((x+-1/x)e^(x^2-2ln(x)))dx. Simplify e^{\left(x^2-2\ln\left|x\right|\right)} by applying the properties of exponents and logarithms. Rewrite the integrand \left(x+\frac{-1}{x}\right)x^{-2}e^{\left(x^2\right)} in expanded form. Expand the integral \int\left(x^{-1}e^{\left(x^2\right)}-x^{-3}e^{\left(x^2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{-1}e^{\left(x^2\right)}dx results in: \frac{1}{2}Ei\left(x^2\right).
