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Question

How do you find the integral of sinx.tanxdx ?


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Solution

Compute the required value.

We know that tanx can be expressed as, tanx=sinxcosx

sinx.tanxdx=sinx.sinxcosxdx

=sin2x.secxdx

=secx1-cos2xdxsin2x=1-cos2x

=secx-cosxdx

=secxdx-cosxdx

=ln(tanx+secx)-sinx+C secxdx=ln(tanx+secx),cosxdx=sinx

Hence the value of sinx.tanxdx is ln(tanx+secx)-sinx+C.


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