Question
1) Evaluate the integral: (csc 2 (x) + cos(x))dx Every time I try to solve the problem, i come up with the answer: -(1/cos(x)) (1/sin(x))
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: (xe2x/ (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
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