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Integral Calculus> evaluate ∫ (2(x)^4 +7(x)^3+ 6(x)^2)/x^2 +...

question mark

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

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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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