1) Evaluate the integral: (csc²(x) + cos(x))dx

Every time I try to solve the problem, i come up with the answer: -(1/cos(x)) (1/sin(x)) - sin(x) + C But the correct answer is: -cot(x) - sin(x) + C

Here is my work:

(1/sin²(x))dx -cos(x)dx u=sin(x) du/cos(x) = dx

(1/u²)(du/cos(x)) - sin(x)

(1/cos(x))(1/u²)du - sin(x)

(1/cos(x))(-1/u) - sin(x)

-(1/cos(x))(1/sin(x)) - sin(x) + C

2) Find the indefinite integral: (xe^2x/ (2x+1)²) dx

I'm assuming I find the solution by using integration by parts

This is what I came up with:(x+ (1/2e)/(2x+1))dx + -((1/2e)/(2x+1)²)dx

and this is also where i am stuck