How do you find the integral of ∫sinx.tanxdx ?
Compute the required value.
We know that tanx can be expressed as, tanx=sinxcosx
∫sinx.tanxdx=∫sinx.sinxcosxdx
=∫sin2x.secxdx
=∫secx1-cos2xdx∵sin2x=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.