Help with IntegralS! Very Important! Quick!

1. May 5, 2007

Student from UA

Hi! Im poor student from Ukraine! Im writing u becouse u are my last chans!
So I need to do homewofk for monday-tuesday. I have problem becouse i was ill and siting at home during lessons about integration! Sorry for My bad English, but i hope u understad.
So i have 10 integrals! At first i search in intarnet some calcus. I found www.cal101.com [Broken] But it give me only result. Function step by step only for money! But i havent! what i must do? =( Thanks God and Google I find U.
I hope u help me becouse its very very important to me.
So 10 integrals(all indefine):
1) (2*(x^(1/3))+3*x*(x^(1/2)))/(x^(1/4))
2) ((x^3+1)^(1/4))*(x^2)
3) (1-2*sinx)/(cosx^2)
4) 2^(x/2)
5) dx/((4-x^2)^(1/2))
6) tg(x^(1/2))*(dx/x^(1/2))
7) dx/((4+x^2)^(1/2))
8) (sin(x/2))^2
9) lnx/(x^(1/2))
10) (1-3x)cos2x
They are in Attach Files!

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2. May 5, 2007

cristo

Staff Emeritus
Hi and welcome to the forums. Firstly please note that the forum rules state that you must show some work before we can help. What do you know about integration? Have you had a go at any of the questions?

Also, in future, please note that we have homework forums specifically for these type of question.

3. May 5, 2007

Student from UA

I agree with u, - I must do homework not u. Ive just start so in atach u can see 1 an 2 . But i think it isnt right/

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4. May 5, 2007

cristo

Staff Emeritus
1. $$x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}$$

2. Your technique is incorrect. Have you come across integration by substitution? Try the substitution y=x^3+1

5. May 5, 2007

Student from UA

U know if i werent ill all 2 week, i do home work well. Im have good marks 87 of 100. I have never ask people to help me in algebra.. butt know. very X situation. I havent free time to learn intaegrals, becouse now i do years work in Descrete Mathematic. =( Next week i must to complete. Thanks God with Descrete mathematica im good.

6. May 5, 2007

Student from UA

O fu.... Really. Its child mistake... Oh.... Sorry. Hm . Im trying again.

7. May 5, 2007

cristo

Staff Emeritus
Ok. Don't worry, and don't let youself get stressed; it's only homework, not a life and death situation! Try and calm down a little, and take your time. Then you're less likely to make mistakes.

8. May 5, 2007

Student from UA

About 1. Im stuck in a middle. I have result (72x^(13/12))+(52x^(9/4)))/39. Is it right?

9. May 5, 2007

Student from UA

You know i do right the 1st =) I compare it with cal101 result. Cal101 make other version but in result we have right rsult =) He he I love integrals!

10. May 5, 2007

Student from UA

But.. Remain else 9 . What to do?

11. May 5, 2007

Student from UA

ANd u now... U have 3 pm. But im in 0.13 AM =( Really want go to sleep but How? =( when i think, what will hapen with me if i will not complete the task....

12. May 5, 2007

Student from UA

About the 2. In calc101.com result (atach file) diferent only with x^3 (see my version) . So where i do mistake , and in the and have misterios x^3

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13. May 5, 2007

Crosson

How did you get in this bad situation?

14. May 5, 2007

Student from UA

I much powerfully was ill, and has missed nearly 2 weeks lessons. Beside me was a temperature from 35.6 before 39. ANd i couldnt do anything.

15. May 5, 2007

cristo

Staff Emeritus
Right: question 1. $$\int\frac{2x^{1/3}+3x^{3/2}}{x^{1/4}}dx=\int 2x^{1/2}+3x^{5/4} dx$$ Can you integrate this using the rule for fractional powers?

question 2. $\int(x^3+1)^{1/4}x^2 dx$.
Are you familiar with the method of substitution? If so use the substitution y=x^3+1; this gives dy=3x^2dx. Substituting into the integrand gives $$\int y^{1/4}\frac{dy}{3}$$. Can you solve this? The substituting in for x will give you the solution.

16. May 5, 2007

cristo

Staff Emeritus
A few more hints for the ones I can see how to do immediately!

5&7 will be some trig subsitutions. For 5 let x=2sinu, for 7 let x=2tanu.
8. looks like it will be do-able using the double angle formula to express it in terms of sinx (or cosx)
10. use integration by parts.

That should give you a bit to work on, I'll have a look at the others in more detail when I've got time [or if anyone else is reading, feel free to help, of course!!!]

17. May 5, 2007

Crosson

How much do you know about integration?

18. May 6, 2007

Student from UA

To Crosson:
Not much. =(. But I trying to rescue the situation.
Ive just get up. Now i start to do the second. And when i finish it, try to make 5&7.

19. May 6, 2007

Student from UA

THX . I ve done the second! Integration is interesting .... but.. now i just start to do 5... =9

20. May 6, 2007

Student from UA

Hm see the 5. I can`t stand, what i do wrong. help

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