Question

can anyone help me to fin itegration of sin(2x)*sec^5(2x)

Answer 1

I find it easiest to begin by converting sec to 1/cos, so we begin with\[\sin (2x)\frac{ 1 }{ \cos ^5(2x) }\]Now we can easily see this problem is a candidate for u-substitution because the derivative of cos is -sin. We choose u=cos(2x) and that means du=-2sin(2x). The new formula is\[-\frac{ du }{ 2 }u ^{-5}=-\frac{ 1 }{ 2 }u ^{-5}du\]I'm guessing you know how to finish the solution from here.