x cosec 8/3 x dx is equal to -

Maths Indefinite Integral General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

–

tan –8/3 x + 3 tan –2/3 x + c

–

tan –5/3 x + 3 tan 1/3 x + c

tan –8/3 x + 3 tan –2/3 x + c

–

tan –8/3 x – 3 tan –2/3 x + c

Text Solution

Verified by Experts

The correct answer is:

We have, I = x cosec 8/3 x dx

= dx = x sin –8/3 x dx

Since – = –4, which is an even integer. So, we divide both numerator and denominator by cos 4 x.

∴ I = dx

= sec 2 x dx = dt where t = tan x

= dt = – + c

= – tan 1/3 x + c.

Hence is the correct answer.

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