My Questions

1. INT(tan 4^x) dx

2. INT ( (3x+4)/(x^2+1)^2 ) dx

thank you.

2. Originally Posted by pinsim

1. INT(tan 4^x) dx
is it tan(4x) or tan^4(x)

i'll assume the latter since the first would be too easy

int{tan^4(x)}dx
= int{tan^2(x)*tan^2(x)}dx
= int{(sec^2(x) - 1)*tan^2(x)}dx .......trig identity: 1 + tan^2(x) = sec^2(x)
= int{tan^2(x)sec^2(x) - tan^2(x)}dx ...........i multiplied out
= int{tan^2(x)sec^2(x)}dx - int{tan^2(x)}dx ..............split the integral in 2

for the first: int{tan^2(x)sec^2(x)}dx, we proceed by substitution
let u = tan(x)
=> du = sec^2(x) dx
so our integral becomes
int{u^2}du
= (1/3)u^3
= (1/3)tan^3(x)

for the second part: int{tan^2(x)}dx
= int{sec^2(x) - 1}dx .............the same identity
= tan(x) - x

so int{tan^2(x)sec^2(x)}dx - int{tan^2(x)}dx = (1/3)tan^3(x) - tan(x) + x + C

3. still working on the second problem...

4. ## Questions

1. tan 4^x dx ( x is a exponent of 4)

5. Originally Posted by pinsim
1. tan 4^x dx ( x is a exponent of 4)
oh, darn it

6. Originally Posted by pinsim
My Questions

1. INT(tan 4^x) dx

2. INT ( (3x+4)/(x^2+1)^2 ) dx

thank you.
Well the first one has no primitive.

But the second one has, jeje

Just split the integral in two, then you must solve one by substitution and the another one by trigonometric substitution.

7. Originally Posted by Krizalid
Well the first one has no primitive.

But the second one has, jeje

Just split the integral in two, then you must solve one by substitution and the another one by trigonometric substitution.
yeah, i think the same for the first..and for the second, but i was running into problems for the trig substituion part

8. yes i tried but can't solve it .

9. Well, I've got a solution for de second one...

Like I said, split in two integrals and solve one by substitution, and the another one by trigonometric substitution, it's not hard, just set x = tan u and then it's done...

10. When you try the trig. substitution, you'll have to integrate cos² u, but instead to integrate by parts, remember that cos² u = (1 + cos 2u)/2, which is more easy to integrate.

11. heyy budiess ,
thanks first of all for the second Question.
But can you help me for the first one..

12. Originally Posted by pinsim
heyy budiess ,
thanks first of all for the second Question.
But can you help me for the first one..
as Krizalid said, the first one does not have a solution in terms of elementary functions (we don't think). are you sure it's not a typo?

13. the problem is ;

INT tan 4^x dx ( x is a exponent of 4)

14. Originally Posted by pinsim
the problem is ;

INT tan 4^x dx ( x is a exponent of 4)
yeah, it has no solution that we can compute at this point