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What integration techniques can be used for more complicated questions

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Most integration techniques are just clever substitutions or integration by parts. But also keep in mind that many reasonable looking functions can't be reasonably integrated (in the sense that they don't admit an elementary antiderivative). This is the case for your example. If there were no exponential factor then you could just use a trigonometric substitution, but with the e^(x) there you won't be able to find an antiderivative.
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That doesn't have an antiderivative in standard functions.

If you have a product of functions, try either a change of variable substitution, or integration by parts.
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