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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

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

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

$=\frac{t^{4}}{4}+c$

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

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