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Grade 12Integral Calculus

evaluate
∫ (x^6 + 1)/(x^2 +1) dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int \frac{x^6+1}{x^2+1}dx$
$I = \int \frac{(x^4-x^2+1)(x^2+1)}{x^2+1}dx$
$I = \int (x^4-x^2+1)dx$
$I = \int x^4dx-\int x^2dx+\int dx$
$I = \frac{x^5}{5}-\int x^2dx+\int dx$
$I = \frac{x^5}{5}-\frac{x^3}{3}+\int dx$
$I = \frac{x^5}{5}-\frac{x^3}{3}+x + c$

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