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integrate the following integral ∫ x^3/x-2 dx

 
integrate the following integral
∫ x^3/x-2 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-2}dx
I = \int \frac{x^3-8+8}{x-2}dx
I = \int \frac{x^3-8}{x-2}dx+\int \frac{8}{x-2}dx
I = \int \frac{(x-2)(x^2+4+2x)}{x-2}dx+\int \frac{8}{x-2}dx
I = \int (x^2+4+2x)dx+\int \frac{8}{x-2}dx
I = \frac{x^3}{3}+x^2+4x+\int \frac{8}{x-2}dx
I = \frac{x^3}{3}+x^2+4x+8log(x-2)+c

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