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I am helping my teenager son. So far I have been able to answer all his questions, and to solve all the problems he has had problems with. Except this one.

$\int{{3^x}{e^x}dx}$

Please, help me keep my success track and my son's confidence.

2 Answers 2

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Hint: try rewriting $3^x$ as $e^{x \ln 3}$.

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    @moron thanks! didnt realize this truth. +12010-12-17
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Why not simply $\int 3^x e^x \mathrm dx = \int (3e)^x \mathrm dx = \frac{(3e)^x}{\ln(3e)} + Constant$

To see that $\int (3e)^x \mathrm dx = \frac{(3e)^x}{\ln(3e)}+C$, You can differentiate $(3e)^x$ i.e. Let

$y = (3e)^x$

$\ln y = x \ln(3e)$

$ \mathrm dy/\mathrm dx = y \ln(3e) = (3e)^x \ln(3e)$

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    @J.M., deleting a comment on which other comments depend leads, more often than not, to more confusion instead of less. Because now picakhu's comment (and any further comment) is erroneous.2011-02-24