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evaluate ∫ (2(x)^4 +7(x)^3+ 6(x)^2)/x^2 + 2x dx

evaluate
∫ (2(x)^4 +7(x)^3+ 6(x)^2)/x^2 + 2x 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{2x^4+7x^3+6x^2}{x^2+2x}dx
I = \int \frac{x^2}{x}.\frac{2x^2+7x+6}{x+2}dx
I = \int (x).\frac{2x^2+4x+3x+6}{x+2}dx
I = \int \frac{x(2x+3)(x+2)}{x+2}dx
I = \int (2x^2+3x)dx
I = \frac{2x^3}{3}+\frac{3x^2}{2}+c

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