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# P3-Integration AHHHHHH watch

1. Integral of (Secx)^4

Well I figured I could make ir 1+(tanx)^4
Then say 1+(sinx/cosx)^4....then use a substitution, but it doesnt work because of that annoying ^4 bit ahhh! any ideas?
Integral of (Secx)^4

Well I figured I could make ir 1+(tanx)^4
Then say 1+(sinx/cosx)^4....then use a substitution, but it doesnt work because of that annoying ^4 bit ahhh! any ideas?
That isn't right.

sec^2 x = 1 + tan^2 x

=> sec^4 x = (1 + tan^2 x)^2
3. lol omg, i am so stupid! thanks nylex!!
4. sec^4X = sec²X(1-tan²X) = sec²X - sec²Xtan²X

Integrate these separately...

That's right, right?
5. (Original post by XTinaA)
sec^4X = sec²X(1-tan²X) = sec²X - sec²Xtan²X

Integrate these separately...

That's right, right?
Yea that's right, but how the hell you're supposed to integrate sec²Xtan²X, i don't know!

By parts just for the (INT (sec²Xtan²X)) bit, i get :

= tanXtan²X - (INT (2sec²Xtan²X))

right?! but then how do you integrate THAT?!
6. (Original post by Sahir)
Yea that's right, but how the hell you're supposed to integrate sec²Xtan²X, i don't know!

By parts just for the (INT (sec²Xtan²X)) bit, i get :

= tanXtan²X - (INT (2sec²Xtan²X))

right?! but then how do you integrate THAT?!
**** sorry just realised if f(x) = tanX then it's the integral of (f '(x))(f(x)^2)

Cool no probs.
7. (Original post by Sahir)
Yea that's right, but how the hell you're supposed to integrate sec²Xtan²X, i don't know!

By parts just for the (INT (sec²Xtan²X)) bit, i get :

= tanXtan²X - (INT (2sec²Xtan²X))

right?! but then how do you integrate THAT?!
Perhaps:

sec²Xtan²X = (secXtanX)²
Remember that d(secX)/dX = secXtanX, substitution?
8. (Original post by Sahir)
Yea that's right, but how the hell you're supposed to integrate sec²Xtan²X, i don't know!

By parts just for the (INT (sec²Xtan²X)) bit, i get :

= tanXtan²X - (INT (2sec²Xtan²X))

right?! but then how do you integrate THAT?!
Judging by what you've written, you don't need to - think about it!

Ben
9. (Original post by XTinaA)
Perhaps:

sec²Xtan²X = (secXtanX)²
Remember that d(secX)/dX = secXtanX, substitution?
Yea see above, lol. Thanks anyway..
10. (Original post by Ben.S.)
Judging by what you've written, you don't need to - think about it!

Ben
Judging by what i've what what what.. y'what mate?!
11. (Original post by Sahir)
Yea see above, lol. Thanks anyway..
Ah just saw it, nice. This is great, more learning
12. (Original post by XTinaA)
sec^4X = sec²X(1-tan²X) = sec²X - sec²Xtan²X

Integrate these separately...

That's right, right?
sec^2x - sec^2xtan^2x = Integral of sec^2x - Integral of sec^2xtan^2x

= tanx - Integral of sec^2xtan^2x

u = tanx
du/dx = sec^2x

Integral u^2 du

=u^3/3 = tan^3x/3

Integral is there = tanx - tan^3x/3 + C

13. (Original post by Sahir)
Judging by what i've what what what.. y'what mate?!
Well - you've written an equation. You don't actually need to integrate!

Ben
14. (Original post by imasillynarb)
sec^2x - sec^2xtan^2x = Integral of sec^2x - Integral of sec^2xtan^2x

= tanx - Integral of sec^2xtan^2x

u = tanx
du/dx = sec^2x

Integral u^2 du

=u^3/3 = tan^3x/3

Integral is there = tanx - tan^3x/3 + C

Differentiate and see!

Ben
15. (Original post by Ben.S.)
Differentiate and see!

Ben
Yes, it's correct.

Ben
16. We rock!
17. (Original post by XTinaA)
We rock!
Pfft, I do, dunno about you mate!
18. (Original post by Sahir)
Judging by what i've what what what.. y'what mate?!
He means....
(Original post by Sahir)
Yea that's right, but how the hell you're supposed to integrate sec²Xtan²X, i don't know!

By parts just for the (INT (sec²Xtan²X)) bit, i get :

= tanXtan²X - (INT (2sec²Xtan²X))

right?! but then how do you integrate THAT?!
(INT (sec²Xtan²X)) = tanXtan²X - (INT (2sec²Xtan²X))

=> 3(INT (sec²Xtan²X)) = tanXtan²X

=> (INT (sec²Xtan²X)) = tanXtan²X/3
19. (Original post by elpaw)
He means....

(INT (sec²Xtan²X)) = tanXtan²X - (INT (2sec²Xtan²X))

=> 3(INT (sec²Xtan²X)) = tanXtan²X

=> (INT (sec²Xtan²X)) = tanXtan²X/3
I was getting them to think! Damn you Elpaw, your children and your children's children!!! No offence.

Ben
20. (Original post by imasillynarb)
Pfft, I do, dunno about you mate!
Less of the cheek you!

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