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integrate the following integral ∫ (x^4 + 3) / (x^2 + 1) dx

 
integrate the following integral
∫ (x^4 + 3) / (x^2 + 1) 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^4+3}{x^2+1}dx
I = \int \frac{x^4-1+4}{x^2+1}dx
I = \int [\frac{x^4-1}{x^2+1}+\frac{4}{x^2+1}]dx
I = \int (x^2-1)dx+\int \frac{4}{x^2+1}dx
I = \frac{x^3}{3}-x+\int \frac{4}{x^2+1}dx
I = \frac{x^3}{3}-x+4tan^{-1}x+c

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