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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 3 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 3 Maths Textbook Solution.

Answers (1)

Answer:

\int-\frac{1}{1+x}-\frac{1}{2(x+1)^{2}}+C

Given:

\int \frac{x+2}{(x+1)^{3}} d x

Hint:

Use power rule for integration.

Solution:    we have

\int \frac{x+2}{(x+1)^{3}} d x

\begin{aligned} &=\int \frac{x+1+1}{(x+1)^{3}} d x \\ &=\int \frac{x+1}{(x+1)^{3}}+\frac{1}{(x+1)^{3}} d x \end{aligned}

\begin{aligned} &=\int \frac{1}{(x+1)^{2}}+\frac{1}{(x+1)^{3}} d x \\ &=-\frac{1}{x+1}-\frac{1}{2(x+1)^{2}}+c \end{aligned}

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