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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 44 Maths Textbbok Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 44 Maths Textbbok Solution.

Answers (1)

Answer:

I=\frac{1}{4} \tan ^{-1}\left(x+\frac{1}{2}\right)+c

Given:

\int \frac{1}{4 x^{2}+4 x+5} d x

Hint:

To solve this equation we will use split term method.

Solution: 

I=\int \frac{d x}{4 x^{2}+4 x+5}

   I=\int \frac{d x}{4\left(x^{2}+x\right)+5}

I=\int \frac{d x}{4\left(x+\frac{1}{2}\right)^{2}+4}                                        \left[\because\left(x^{2}+\frac{1}{2}\right)^{2}=x^{2}+\frac{1}{4}+\frac{2 x}{2}=x^{2}+x+\frac{1}{4}-\left(\frac{1}{4}\right)\right]

I=\frac{1}{4} \int \frac{d x}{\left(x+\frac{1}{2}\right)^{2}+(1)^{2}}

I=\frac{1}{4} \tan ^{-1} \frac{\left(x+\frac{1}{2}\right)}{1}+\mathrm{c}

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infoexpert21

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