Final Answer
Step-by-step Solution
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Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$
Learn how to solve integrals of exponential functions problems step by step online.
$\int xe^{-\frac{x}{2}}dx$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x/(e^(x/2)))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. We can solve the integral \int xe^{-\frac{x}{2}}dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x), so we must integrate e^{-\frac{x}{2}} a total of 2 times.