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evaluate ∫ (5(x)^4 +12(x)^3 +7(x)^2)/x^2 + x dx

evaluate
∫ (5(x)^4 +12(x)^3 +7(x)^2)/x^2 + x dx

Grade:12

1 Answers

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

I = \int \frac{5x^4+12x^3+7x^2}{x^2+x}dx
I = \int\frac{x^{2}}{x}. \frac{5x^2+12x+7}{x+1}dx
I = \int(x) \frac{5x^2+12x+7}{x+1}dx
I = \int(x) \frac{5x^2+5x+7x+7}{x+1}dx
I = \int(x) \frac{(5x+7)(x+1)}{x+1}dx
I = \int x(5x+7)dx
I = \int (5x^2+7x)dx
I = \frac{5x^3}{3} + \frac{7x^2}{2}+c

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