integration by substitution (1 Viewer)

[jkwii]

i dont know what subs to use for
0.5a
∫ dx/(a^2-x^2)
0

and
pi
∫ dx/(1-cosx)
pi/2

and
pi/2
∫ dx/(4-2cos^2x)
0

 

[independantz]

For the first one, let x=asin@ or acos@, your choice really.

For the second one, try t-formulae i suppose.

T-formulae for the third aswell, or try manipulating using trig.

 

[Iruka]

For the first one, you could use partial fractions.

For the second, try multiplying the numerator and denominator by (1 + cosx).

 

[jkwii]

i can get the 1st one out (although my tutor's answer is 1/Sqrt(3) a^2.

the second one does something stupid - using t=tanx/2 one limit doesnt exist???

help