Integration

Write sin2x as 2sinxcosx,take cos^4x common from the denominator,We'll get the integrand as ∫2tanxsec²x/(1+tan⁴x) now put tanx=t
==>∫ 2tdt/(1+t⁴) ,put t²=u,Now it will be simple to solve

that ncert miscellaneous exercise is really worth doing.... atleast i felt so...

or cos⁴x + sin⁴x = (cos²x+sin²x)² - 2 sin²x cos²x

= 1 - sin²2x/2 = (1+cos²2x)/2

Now put cos 2x = t and integrate