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Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise 18.11 Question 1 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{4} \tan ^{4} x+C

Hint :-  Use substitution method to solve this integral.

Given:\int \tan ^{3} x \cdot \sec ^{2} x d x

Solution: Let I=\int \tan ^{3} x \cdot \sec ^{2} x d x

Put \tan x=t \rightarrow \sec ^{2} x d x=d t then

I=\int t^{3} \cdot \mathrm{dt}                              \text { (if, } \tan x=t \text { ) }

  =\frac{t^{3+1}}{3+1}+C                            \text { (if, } \left.\int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right)


=\frac{\tan ^{4} x}{4}+C \quad(\text { if, } \mathrm{t}=\tan \mathrm{x})



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