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# c4 question on integration by substitution watch

1. integrate
sex^4 dx

u=tanx

i attempted this question and got as far as this

-sec^2 x du

what do i do next or am i on the right lines?
thankx
2. (Original post by diggingupworms)
integrate
sex^4 dx

u=tanx

i attempted this question and got as far as this

-sec^2 x du

what do i do next or am i on the right lines?
thankx
I hope that's not a minus sign you have there!

Do you know an identity connecting sec and tan?
3. (Original post by ghostwalker)
I hope that's not a minus sign you have there!

Do you know an identity connecting sec and tan?
the diffential of tanx is -sec^2 x
so i divded it
4. (Original post by diggingupworms)
the diffential of tanx is -sec^2 x
so i divded it
the differential of tanx is sec^2 x without the -ve sign.
5. (Original post by KeineHeldenMehr)
the differential of tanx is sec^2 x without the -ve sign.
o
yeah so you would get

after

sec^2 x du
6. u = tan x
du/dx = sec^2 x
du = sec^2 x dx

integrate tan x = integrate tan x (sec^2 x ) dx
7. ok,

i'm going to use "S" as an integrating sign just did speed things up.
S (sec^4 x)dx
=S((sec^2 x)(sec^2 x)dx

now with u=tanx

we differentiated du/dx=sec^2x
so du=(sec^2x)dx

so, S((sec^2 x)du

from here just use u^2=tan^2x, (which is your substitution squared on both sides) and the identity tan^2x+1 = sec^2x

should give you S(u^2+1)du - integrate it!

then replace u with your substitution.
8. (Original post by KeineHeldenMehr)
ok,

i'm going to use "S" as an integrating sign just did speed things up.
S (sec^4 x)dx
=S((sec^2 x)(sec^2 x)dx

now with u=tanx

we differentiated du/dx=sec^2x
so du=(sec^2x)dx

so, S((sec^2 x)du

from here just use u^2=tan^2x, (which is your substitution squared on both sides) and the identity tan^2x+1 = sec^2x

should give you S(u^2+1)du - integrate it!

then replace u with your substitution.
THANK YOU! x

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