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Grade 12Integral Calculus

integrate the following integral
∫ (e^x +1)^2 e^x dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int e^{x}(e^{x}+1)^2dx$
$I = \int e^{x}(e^{2x}+1+2e^{x})dx$
$I = \int (e^{3x}+e^{x}+2e^{2x})dx$
$I = \int e^{3x}dx+\int e^{x}dx+2\int e^{2x}dx$
$I = \frac{e^{3x}}{3}+\int e^{x}dx+2\int e^{2x}dx$
$I = \frac{e^{3x}}{3}+e^{x}+2\int e^{2x}dx$
$I = \frac{e^{3x}}{3}+e^{x}+e^{2x}+c$

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