Integrate 6x/(sin^2x) from pi/6 , pi/2

Question

alekos · Answer

why don't you plug in the values and see what result you get?

anonymous · Answer

how to do integral of 6x/(sin^2x)

hero · Answer

http://www.mathsisfun.com/calculus/integration-rules.html

anonymous · Answer

x is not constant how we can take it out....

hero · Answer

Use should use uv substitution for this

anonymous · Answer

ok ..thanks

alekos · Answer

sorry, didn't read your question properly. 
i agree with Hero,  use integration by substitution

ganeshie8 · Answer

yes by  parts,  or if u knw complex numbers,  consider complexifying....

parthkohli · Answer

$$I:=\int \dfrac{6x}{\sin^2x}dx$$$$= \int 6x \cdot \dfrac{1}{\sin^2x}dx$$$$= \int 6x\cdot \csc^2(x)dx$$
$$u = 6x \Rightarrow du = 6dx$$$$v = -\cot(x) \Rightarrow  dv = \csc^2(x) dx\Rightarrow $$
Now,$$I=uv - \int vdu$$$$=-6x\cot x -\int -6\cot(x)dx$$$$= -6x\cot x +6\ln|\sin(x)|+C$$

parthkohli · Answer

I have no idea why it took so long to submit.

parthkohli · Answer

Anyway, that's the antiderivative.