\int \sec ^{3}\theta d\theta=

  • Option 1)

                1/2 [tan \theta sec \theta + log |(tan \theta+ sec \theta)|] + c

  • Option 2)

    1/2 [tan \theta + sec \theta - log|(tan \theta + sec \theta)|] + c

  • Option 3)

    1/2  [tan \theta sec \theta - log |(sec \theta - tan \theta)|] + c

  • Option 4)

    none of these

 

Answers (1)
V Vakul

As we learnt

Integration By PARTS -

Let u and v are two functions then 

\int u\cdot vdx=u\int vdx-\int \left ( \frac{du}{dx}\int vdx \right )dx

- wherein

Where u is the Ist function v is he IInd function

 

 

I                             = ò sec q sec2q dq

                                    = sec q tan q -ò sec q tan2q dq

                                    = sec q tan q - ò sec3 q dq + ò sec q dq

                              \   2I = sec q tan q + log |sec q + tan q| + c

                              Þ  I = 1/2[tan q sec q + log|tan q +  sec q|] + c

 

 


Option 1)

            1/2 [tan \theta sec \theta + log |(tan \theta+ sec \theta)|] + c

Option 2)

1/2 [tan \theta + sec \theta - log|(tan \theta + sec \theta)|] + c

Option 3)

1/2  [tan \theta sec \theta - log |(sec \theta - tan \theta)|] + c

Option 4)

none of these

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