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evaluate ∫ ((x^3 + 8)(x – 1)) / x^2 – 2x + 4 dx

evaluate
∫ ((x^3 + 8)(x – 1)) / x^2 – 2x + 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+8)(x-1)}{x^2-2x+4}dx
I = \int \frac{(x+2)(x^2-2x+4)(x-1)}{x^2-2x+4}dx
I = \int (x+2)(x-1)dx
I = \int (x^2+x-2)dx
I = \int x^2dx+\int x-2\int dx
I = \frac{x^3}{3}+\int x-2\int dx
I = \frac{x^3}{3}+\frac{x^2}{2}-2\int dx
I = \frac{x^3}{3}+\frac{x^2}{2}-2x + c

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