How do you go about this question? $inte^(x+e^(x))dx$

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$inte^(x+e^(x))dx$

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Answer 1 · 2018-03-29T13:28:56

$inte^(x+e^x)"d"x=e^(e^x)+"c"$

$inte^(x+e^x)dx=inte^xe^(e^x)dx$

Let $u=e^(e^x)$ . By the chain rule,

$(du)/dx=d/dxe^(e^x)=d/(de^x)e^(e^x)d/dxe^x=e^xe^(e^x)$

Substituting this into the integral gives

$inte^xe^(e^x)dx=intdu=u+"c"=e^(e^x)+"c"$