Integration question-help needed (1 Viewer)

[lsdpoon1337]

Hi, I am having trouble doing these two questions:

Integrate:

1. (1 + cos 2x)/ (sin 2x)^2

answer given: -0.5(cosec 2x + cot 2x) + c


2. (sin 2x)^2/ (1 + cos 2x)

answer given: x - 0.5sin2x + c

thank you very much

 

[azureus88]

(a) [maths]\int \frac{1+\cos 2x}{\sin^22x}\,dx\\=\int \csc^22x\,dx+\int (\cot x)(\csc x)\,dx\\=-0.5(\csc 2x+\cot 2x)+C[/maths]


(b) [maths]\int \frac{\sin^22x}{1+\cos2x}\,dx\\=\int \frac{1-\cos^22x}{1+\cos2x}\,dx\\=\int (1-\cos2x)\,dx\\=x-0.5\sin2x+C[/maths]