Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals2 Marks
Question
Find the integral: $\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$
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Answer
Let I = $\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$ Separating the terms we get, I = $\int\left(x+5-4 x^{-2}\right) d x$ Applying the formula, $\int x^{n} d x=\frac{x^{n+1}}{n+1}+c$ , gives I = $\int x d x+5 \int 1 d x-4 \int x^{-2} d x$ = $\frac{x^{2}}{2}+5 x-4\left(\frac{x^{-1}}{-1}\right)+C$ = $\frac{x^{2}}{2}+5 x+\frac{4}{x}+C$
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