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Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 114 Maths Textbook Solution.

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Answer: 3 x \sin ^{-1} x+3 \sqrt{1-x^{2}}+C

To solve this question we will use ILATE Method

Given:\int \sin ^{-1}\left(3 x-4 x^{3}\right) d x


\int 3 \sin ^{-1} x d x

I=3 \int 1 \cdot \sin ^{-1} x d x

I=3 \int 1 \cdot \sin ^{-1} x d x


I=3\left[x \sin ^{-1} x-\int \frac{-d t}{2 \sqrt{t}}\right] \ldots \text { applying byparts }

I=3\left[x \sin ^{-1} x+\frac{1}{2} \int t^{-\frac{1}{2}} d t\right]

I=3\left[x \sin ^{-1} x+\frac{1}{2} \frac{t^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C\right)

I=3\left[x \sin ^{-1} x+\frac{1}{2} \frac{\sqrt{t}}{\frac{1}{2}}+C\right]

I=\left[3 x \sin ^{-1} x+3 \sqrt{1-x^{2}}+C\right]


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