How do you use Integration by Substitution to find $\int e^{x} \cdot cos (e^{x}) d x$ $inte^x*cos(e^x)dx$ ?

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How do you use Integration by Substitution to find $\int e^{x} \cdot cos (e^{x}) d x$ $inte^x*cos(e^x)dx$ ?

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Answer 1 · 2014-07-28T16:32:17

$sin (e^{x}) + c$ $sin(e^x)+c$ , where c is a constant

Explanation,

Integration by Substitution,

$\int e^{x} \cdot cos (e^{x}) d x$ $inte^x*cos(e^x)dx$

let's assume $e^{x} = t$ $e^x=t$

then, $e^{x} \cdot d x = d t$ $e^x*dx=dt$

$\int cos (t) d t$ $intcos(t)dt$

$sin (t) + c$ $sin(t)+c$ , where c is a constant

Substituting $t = e^{x}$ $t=e^x$ , we finally get

$sin (e^{x}) + c$ $sin(e^x)+c$ , where c is a constant

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How do you use Integration by Substitution to find $\int e^{x} \cdot cos (e^{x}) d x$ $inte^x*cos(e^x)dx$ ?

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