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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 1 Maths Textbook Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 1 Maths Textbook Solution.

Answers (1)

Answer:

\frac{1}{4} \tan ^{-1} \frac{x^{2}}{2}+C

Given:

\int \frac{x}{4+x^{4}} d x

Hint:

Using \int \frac{d x}{1+x^{2}}

Explanation:

Let \mathrm{I}=\int \frac{x}{4+x^{4}} d x

         =\int \frac{x d x}{(2)^{2}+\left(x^{2}\right)^{2}}                                   \text { [Put } \left.x^{2}=t \Rightarrow 2 x \mathrm{~d} x=\mathrm{dt} \Rightarrow x \mathrm{dx}=\frac{d t}{2}\right]

         \begin{aligned} &=\int \frac{1}{(2)^{2}+t^{2}} \times \frac{d t}{2} \\ &=\frac{1}{2} \int \frac{d t}{t^{2}+2^{2}} \\ &=\frac{1}{2} \cdot \frac{1}{2} \tan ^{-1} \frac{t}{2}+C \ldots \ldots . .\left\{\int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+c\right\} \\ &=\frac{1}{4} \tan ^{-1} \frac{x^{2}}{2}+C \end{aligned}

       

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