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QIANBUSCALC$24\mathrm{.}5\mathrm{.}503.$XP$.$

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Tutorial Exercise

Evaluate the indefinite integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^x\sqrt[\phantom{2}]{8+e^x}dx$

Step $1$

We must decide what to choose for $u.$

If $u=f(x),$ then $du=f^{\text{'}}(x)dx,$ and so it is helpful to look for some expression in ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^x\sqrt[\phantom{2}]{8+e^x}dx$ for which the derivative is also present.

We see that $8+e^x$ is part of this integral, and the derivative of $8+e^x$ is

$,$ which is also present.

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