Final answer to the problem
$e^x\cdot x-e^x-xe^x+e^x=0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Integrate using tabular integration
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- Weierstrass Substitution
- Exact Differential Equation
- Linear Differential Equation
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1
The integral of the exponential function is given by the following formula $\displaystyle \int a^xdx=\frac{a^x}{\ln(a)}$, where $a > 0$ and $a \neq 1$
$\int xe^xdx=xe^x-e^x$
Learn how to solve equations problems step by step online. Solve the differential equation int(xe^x)dx=xe^x-int(e^x)dx. The integral of the exponential function is given by the following formula \displaystyle \int a^xdx=\frac{a^x}{\ln(a)}, where a > 0 and a \neq 1. Solve the integral \int xe^xdx and replace the result in the differential equation. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side.
Final answer to the problem
$e^x\cdot x-e^x-xe^x+e^x=0$
