Question

The integral of 7((cos(x)+sin(x))/(sin(2x))

Answer 1

hint: sin(2x) = 2sin(x)cos(x)

Answer 2

cant you also use sin2x=1/2 cos(2x)

Answer 3

how is sin(2x) = (1/2) cos(2x)?

Answer 4

that trig identity isn't true

Answer 5

oh i think it is (cos(2x)/2) is that not right ?

Answer 6

for integration by parts?

Answer 7

how about this,

7(cosx + sinx)/(2sinx cosx)

= (7/2) [ cosx/(sinx cosx) + sinx/(sinx cosx) ]

= (7/2) (cscx + secx)

can you finish from here?

Answer 8

i just gave you 95% of the answer

Answer 9

okay ill see if i can finish it

Answer 10

how do i figure out what the integral of the csc and sec are ?

Answer 11

7/2((ln(tan(x)+sec(x))-ln(csc(x)+cot(x)))

Answer 12

well, you can look up the basic integral for trig and memorize them.

Just like you memorize that the integral of cos(x) is sin(x).

The integral of cscx is ln(cscx - cotx)