If ∫sec4/3⁡xcosec8/3⁡xdx=a(tan⁡x)−5/3+b(tan⁡x)1/3+C, then 5a+b=

# If $\int {\mathrm{sec}}^{4/3}x{\mathrm{cosec}}^{8/3}xdx=a\left(\mathrm{tan}x{\right)}^{-5/3}+b\left(\mathrm{tan}x{\right)}^{1/3}+C,$ then $5a+b=$

1. A

3

2. B

$-3$

3. C

0

4. D

$-1$

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### Solution:

We have,

The sum of the exponents of  and  is  an even integer. So, we divide both numerator and denominator by ${\mathrm{cos}}^{4}x.$

and $b=3⇒5a+b=0$

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The passage contains a mathematical question involving an integral and its solution, followed by a multiple-choice question asking for the value of an expression based on the solution. The answer to the multiple-choice question is provided.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
If ∫sec4/3⁡xcosec8/3⁡xdx=a(tan⁡x)−5/3+b(tan⁡x)1/3+C, then 5a+b=

# If $\int {\mathrm{sec}}^{4/3}x{\mathrm{cosec}}^{8/3}xdx=a\left(\mathrm{tan}x{\right)}^{-5/3}+b\left(\mathrm{tan}x{\right)}^{1/3}+C,$ then $5a+b=$

1. A

3

2. B

$-3$

3. C

0

4. D

$-1$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

We have,

The sum of the exponents of  and  is  an even integer. So, we divide both numerator and denominator by ${\mathrm{cos}}^{4}x.$

and $b=3⇒5a+b=0$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)
user
The passage contains a mathematical question involving an integral and its solution, followed by a multiple-choice question asking for the value of an expression based on the solution. The answer to the multiple-choice question is provided.

TYPE: SINGLE_QUESTION_WITH_ANSWER