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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 32 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise 18.25 Question 32 Maths Textbook Solution.

Answers (1)

Answer: x\tan \: x+log\left ( \cos \: x \right )-\frac{x^{2}}{2}+c

Given: \int x\tan ^{2}xdx

Hint: \int uvdx=u\int vdx-\int \left ( \frac{d}{dx}u\int vdx \right )dx

Solution:

              \begin{aligned} &I=\int x \tan ^{2} x d x \\ &{\left[\tan ^{2} x=\sec ^{2} x-1\right]} \\ &I=\int x \sec ^{2} x d x-\int x d x \\ &I=x \int \sec ^{2} x d x-\int\left[\frac{d}{d x} x \int \sec ^{2} x d x\right] d x-\frac{x^{2}}{2}+c \\ &I=x \tan x-\int \tan x d x-\frac{x^{2}}{2}+c \\ &I=x \tan x+\log (\cos x)-\frac{x^{2}}{2}+c \end{aligned}

 

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