Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 78 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 78 Maths Textbook Solution.

Answers (1)

Answer:

\ln |\sec x+\tan x|-\sin x-\frac{\sin 3 x}{3}-\frac{\sin ^{5} x}{5}+c

Hint:

To solve the given equation we have to split the sin? x term in sin? x.sin² x.

Given:

\int \frac{\sin ^{6} x}{\cos x} d x

Solution:

I=\int \frac{\sin ^{6} x}{\cos x} d x

   =\int \frac{\sin ^{4} x \sin ^{2} x}{\cos x} d x=\int \frac{\sin ^{4} x}{\cos x}\left(1-\cos ^{2} x\right) d x

 =\int \frac{\sin ^{4} x}{\cos x} d x-\int \frac{\sin ^{4} x \cos ^{2} x}{\cos x} d x

  =\int \frac{\sin ^{4} x}{\cos x} d x-\int \sin ^{4} x \cos x d x

=\int \frac{\sin ^{2} x\left(1-\cos ^{2} x\right)}{\cos x} d x-\int t^{4} d t

 =\int \frac{\sin ^{2} x}{\cos x} d x-\int \sin ^{2} x \cos x d x-\frac{t^{5}}{5}

=\int \frac{\left(1-\cos ^{2} x\right)}{\cos x} d x-\int t^{2} d t-\frac{\sin ^{5} x}{5}

=\int \frac{1}{\cos x} d x-\int \cos x d x-\frac{t^{8}}{3}-\frac{\sin ^{5} x}{5}

=\int \sec x d x-\sin x-\frac{\sin 3 x}{3}-\frac{\sin ^{5} x}{5}

=\ln |\sec x+\tan x|+\left(-\sin x-\frac{\sin 3 x}{3}-\frac{\sin ^{5} x}{5}\right)+c

=\ln |\sec x+\tan x|-\sin x-\frac{\sin 3 x}{3}-\frac{\sin ^{5} x}{5}+c

 

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question