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Integration of (1+tanx/1-tanx) dx

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Integration of (1+tanx/1-tanx) dx

Posted by Rekha Maurya 7 years, 6 months ago

CBSE > Class 12 > Mathematics

2 answers

Souvik Debnath 7 years, 6 months ago

On the 2nd step- {(cosx+sinx)/cosx}/{(cosx-sinx)/cosx} dx

Souvik Debnath 7 years, 6 months ago

Convert tanx into sinx/cosx. So, integration of (cosx+sinx/cosx / cosx-sinx/cosx) dx. Now remove cosx. So, integration of (cosx+sinx / cosx-sinx) dx. Let cosx+sinx=t, or, (-sinx+cosx) dx=dt. Now in the integration, put the above placements. So integration of (1/t) dt = log t. Put the value of t = cosx+sinx.

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