Evaluate (3 x^2-5 )^2 d x - Vidyadip

Question

Evaluate $\int\left(3 x^2-5\right)^2 d x$

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Answer

$\text { Let } I =\int\left(3 x^2-5\right)^2 d x$
$=\int\left(9 x^4-30 x^2+25\right) d x$
$=9 \int x^4 d x-30 \int x^2 d x+25 \int d x$
$=9\left(\frac{x^5}{5}\right)-30\left(\frac{x^3}{3}\right)+25 x+ c$
$\therefore I =\frac{9}{5} x^5-10 x^3+25 x+ c $

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