Question

integrate sec^4x sqrt(1+tanx) dx

Answer 1

http://www.wolframalpha.com/input/?i=integrate+%28sec%28x%29%29%5E4*sqrt%281%2Btanx%29+dx

Answer 2

hope it is something you are looking for

Answer 3

wolfram doesn't help me understand the problem please explain the steps

Answer 4

click show steps.. there are 2 times of substitute

Answer 5

i want to view another way of doing it and not use 2 sub

Answer 6

can you continue please

Answer 7

i just stucked give me few mins

Answer 8

okay no problem thank you

Answer 9

oh sorry let tanx +1 = t
secx^2dx = dt

(1+(t-1)^2)t^1/2

(1+t^2+1-2t)t^1/2

{2t^1/2+t^5/2-2t^3/2}dt

4/3t^3/2+2/7t^7/2-4t^5/2 +c

now put t = tanx + 1
you will get answer

Answer 10

you need to draw this out, there are too many numbers i am sorry

Answer 11

how can (1+(t-1)^2)t^1/2 be the next step if you subsituted wouldnt it be t^2 sqrt(t)

Answer 12

check attachment

Answer 13

oh i see what you did, but i was wondering how come the 1+tan^2x cannot become U^2 as well because U=1+tan^2x

Answer 14

sorry but i didn't get it what u said

Answer 15

i let 1+tanx = t

Answer 16

nvm, i got it thank you

Answer 17

welcome