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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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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