Question

integration of sin2x/1+sin^2 x dx is​

Answer 1

Answer:

${x}^{2} + (x / 2) - { sin(2x) / 4} \: + c$

For sin2(X), we will use the cos double angle formula:

cos(2X) = 1 - 2sin2(X)

The above formula can be rearranged to make sin2(X) the subject:

sin2(X) = 1/2(1 - cos(2X))

You can now rewrite the integration:

∫sin2(X)dX = ∫1/2(1 - cos(2X))dX

Because 1/2 is a constant, we can remove it from the integration to make the calculation simpler. We are now integrating:

1/2 x ∫(1 - cos(2X)) dX = 1/2 x (X - 1/2sin(2X)) + C