$\displaystyle \int x^{-3} e^{-2 \over x} dx$ Couldn't figure out what substitution to use for this one. Thanks.
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Hello ! Originally Posted by chopet $\displaystyle \int x^{-3} e^{-2 \over x} dx$ Couldn't figure out what substitution to use for this one. Thanks. Use the substitution $\displaystyle t=-\frac 2x$ $\displaystyle \dots \implies dx=\frac 12 \cdot x^2 \ dt$ And you will see that the integral is $\displaystyle -\frac 14 \ \int t e^t \ dt$ And here, use integration by parts
use ILATE method that will give solution very easily
Thanks guys. Sometimes when we subst, we get the whole exp term, seomtimes just the power. Substitution is really an art.
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