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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 2 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 2 Maths Textbook Solution.

Answers (1)

Answer:

x+\frac{x^{2}}{2}+\frac{x^{8}}{3}+\frac{x^{4}}{4}+c

Hint:

Use the formula a^{2}-b^{2}=(a-b)(a+b)

Solution:    we have

\begin{aligned} &=\int \frac{1-x^{4}}{1-x} d x \\ &=\int \frac{\left(1-x^{2}\right)\left(1+x^{2}\right)}{1-x} d x \\ &=\int \frac{(1-x)(1+x)\left(1+x^{2}\right)}{1-x} d x \\ &=\int(1+x)\left(1+x^{2}\right) d x \\ &=\int 1+x^{2}+x+x^{3} d x \\ &=x+\frac{x^{3}}{3}+\frac{x^{2}}{2}+\frac{x^{4}}{4}+c \\ &=x+\frac{x^{2}}{2}+\frac{x^{3}}{3}+\frac{x^{4}}{4}+c \end{aligned}

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