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integrate the following integral ∫ (x + 3) / (x + 1)^4 dx

 
integrate the following integral
∫ (x + 3) / (x + 1)^4 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{x+3}{(x+1)^{4}}dx
I = \int \frac{x+1+2}{(x+1)^{4}}dx
I = \int [\frac{1}{x+4}+\frac{2}{(x+1)^{4}}]dx
I = \int \frac{1}{x+4}dx+\int \frac{2}{(x+1)^{4}}dx
I = log(x+4)+\int \frac{2}{(x+1)^{4}}dx
I = log(x+4)- \frac{2}{3(x+1)^3}+c

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