Math Help - Integration complicated problems

1. Integration complicated problems

SORRY i really don't know how to put these symbols such as Integral sign ,

1. Integrate for SEC X/3 DX FROM (-PI) --> (PI)

( I think these problems are using substitution to solve but I just can't work it out like how to put them together to solve.

2. Integrate for csc(x-pie) dx from ( from 3pi/2 ---> 7pie/4 )

3. Integrate for dx/ of (1- 9x^2 ) from ( 0 ---> 1/6 )

4. Integrate for 6 DX / X √ OF 25X^2 -1 FROM (2(5√3) ---> 2/5

5. Integrate for sec piex DX from ( 0 ---> 1/4 )

Please tell me how to start and I can solve the rest . Thank you

2. for the first just remember that the integral for sec(x) is ln(abs(sec(x)+tan(x)))

for the second remember that integral for csc(x) is ln(abs(csc(x)-cot(x)))

for the third you can either do simple arcsin sub or even trig sub

for the fourth you can do arcsec sub or even trig sub again

the 5th is really the same as the 1st again