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Integral Calculus> integrate the following integral ∫ (x^4 +...

question mark

integrate the following integral
∫ (x^4 + 3) / (x^2 + 1) dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{x^4+3}{x^2+1}dx$
$I = \int \frac{x^4-1+4}{x^2+1}dx$
$I = \int [\frac{x^4-1}{x^2+1}+\frac{4}{x^2+1}]dx$
$I = \int (x^2-1)dx+\int \frac{4}{x^2+1}dx$
$I = \frac{x^3}{3}-x+\int \frac{4}{x^2+1}dx$
$I = \frac{x^3}{3}-x+4tan^{-1}x+c$

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