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Indefinite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integration1 Mark
Question
Integrate the following functions w.r.t. x:

$2 x^3-5 x+\frac{3}{x}+\frac{4}{x^5}$

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Answer

$\begin{array}{c}\int\left(2 x^3-5 x+\frac{3}{x}+\frac{4}{x^5}\right) d x \\ =2 \int x^3 d x-5 \int x d x+3 \int \frac{1}{x} d x+4 \int x^{-5} d x\end{array}$

$=2\left(\frac{x^4}{4}\right)-5\left(\frac{x^2}{2}\right)+3 \log |x|+4\left(\frac{x^{-4}}{-4}\right)+c$

$=\frac{x^4}{2}-\frac{5}{2} x^2+3 \log |x|-\frac{1}{x^4}+c$

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