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evaluate ∫ (x^5 + x^-2 + 2)/x^2 dx

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

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