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Integration (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)1 Mark
Question
Evaluate $\int\left(3 x^2-5\right)^2 d x$
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Answer

$
\begin{aligned}
& \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 1 d x \\
& =9\left(\frac{x^5}{5}\right)-30\left(\frac{x^3}{3}\right)+25 x+c \\
& =\frac{9 x^5}{5}-10 x^3+25 x+c
\end{aligned}
$

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