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evaluate ∫ (x^6 + 1)/(x^2 +1) dx

evaluate
∫  (x^6 + 1)/(x^2 +1) dx

Grade:12

1 Answers

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

I = \int \frac{x^6+1}{x^2+1}dx
I = \int \frac{(x^4-x^2+1)(x^2+1)}{x^2+1}dx
I = \int (x^4-x^2+1)dx
I = \int x^4dx-\int x^2dx+\int dx
I = \frac{x^5}{5}-\int x^2dx+\int dx
I = \frac{x^5}{5}-\frac{x^3}{3}+\int dx
I = \frac{x^5}{5}-\frac{x^3}{3}+x + c

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