How do you evaluate the integral $\int e^{x} {(e^{x} + 1)}^{3}$ $int e^x(e^x+1)^3$ ?

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Answer 1 · 2017-01-19T14:09:08

$\frac{1}{4} {(e^{x} + 1)}^{4} + C$ $1/4(e^x+1)^4+C$ .

Suppose that (e^x+1)=t :. e^xdx=dt#

Hence, $\int e^{x} {(e^{x} + 1)}^{3} d x = \int {(e^{x} + 1)}^{3} e^{x} d x$ $inte^x(e^x+1)^3dx=int(e^x+1)^3e^xdx$

$= t^{3} d t = \frac{t^{4}}{4}$ $=t^3dt=t^4/4$

$= \frac{1}{4} {(e^{x} + 1)}^{4} + C$ $=1/4(e^x+1)^4+C$ .

How do you evaluate the integral int e^x(e^x+1)^3∫ex(ex+1)3int e^x(e^x+1)^3?