How can I solve this integral using integration by parts?

[jacy]

Hi ,
I am having trouble integrating this problem.

Integrate x^2 sin(x^2) dx

Here is what i did. I used the substitution method.

u = x^2 sqrt u = x
du = 2x dx
du/2x = dx

du/2 sqrt u = dx since sqrt u = x

substituting this in the equation

u sin(u) du/2 sqrt u

Now i don't know how to integrate this. Please help, thanks.

 

[Townsend]

Hi ,
I am having trouble integrating this problem.

Integrate x^2 sin(x^2) dx

I don't think the antiderivative of your integrand is an elementary...but I don't really know for sure.

 

[amcavoy]

I believe you're correct. My computer cannot calculate it.

 

[jacy]

I believe you're correct. My computer cannot calculate it.

Thanks 4 ur time. Do u think that problem is wrong.

 

[Townsend]

Thanks 4 ur time. Do u think that problem is wrong.

The problem is fine...it's just that you cannot find an elementary antiderivative as a solution.

 

[GCT]

where'd you obtain the problem?

 

[amcavoy]

It would work if the integrand was $x\sin{x^{2}}$.

 

[jacy]

where'd you obtain the problem?

Thanks for looking at the problem. My teacher gave this problem on the exam. How can we solve this.

 

[Tony11235]

Integration by parts might be possible, but my computer and my TI 89 cannot compute it, so there's probably not a simple antiderivative. And you were given this problem on a test?

 

[jacy]

Integration by parts might be possible, but my computer and my TI 89 cannot compute it, so there's probably not a simple antiderivative. And you were given this problem on a test?

Thanks, do u think the substitution method that i used will work. This wasn't the only one there were 3 more.

 

[amcavoy]

Are you sure it wasn't asking you to evaluate it as a definite integral numerically? That's the only way I can see doing this.

 

[jacy]

Are you sure it wasn't asking you to evaluate it as a definite integral numerically? That's the only way I can see doing this.

No it isn't a definite integral. It's tough one. Hopefully the teacher should provide the solution today. If he does, then can i post the solution in here, thanks.

 

[whozum]

[itex]\int x^2\sin(x^2) dx [/tex]<br /> <br /> [itex]\int x^2\sin(x^2) dx = \frac{-x}{2}\cos(x^2) + \frac{1}{2} \int \cos(x^2) dx [/tex][/itex][/itex]

 

[quantumdude]

[itex]\int x^2\sin(x^2) dx [/tex]<br /> <br /> [itex]\int x^2\sin(x^2) dx = \frac{-x}{2}\cos(x^2) + \frac{1}{2} \int \cos(x^2) dx [/tex][/itex][/itex]

[itex][itex] <br /> True, but now what's $\frac{1}{2} \int \cos(x^2) dx$?<br /> <br /> jacy, the initial response you received was correct. Your integrand doesn't have an elementary antiderivative. 10 bucks says that the problem was supposed to be $\int x\sin(x^2) dx$.[/itex][/itex]

 

[whozum]

True, but now what's $\frac{1}{2} \int \cos(x^2) dx$?

jacy, the initial response you received was correct. Your integrand doesn't have an elementary antiderivative. 10 bucks says that the problem was supposed to be $\int x\sin(x^2) dx$.

Its not elementary i was just trying it out and seeing how far I could get, but figured I'd just post it anyway.

 

[Jameson]

Here's the answer from Mathematica in case anyone was wondering. I agree, it was probably supposed to be $$\int x\sin{(x^2)}dx$$.

 

[jacy]

True, but now what's $\frac{1}{2} \int \cos(x^2) dx$?

jacy, the initial response you received was correct. Your integrand doesn't have an elementary antiderivative. 10 bucks says that the problem was supposed to be $\int x\sin(x^2) dx$.

I don't think so it was a typo. This problem was on the exam, thanks.

 

[whozum]

I don't think so it was a typo. This problem was on the exam, thanks.

Was the problem asking to find the derivative of that function?

 

[jacy]

Was the problem asking to find the derivative of that function?

We have to find the anti derivative of that function. Today the teacher said that he made a typo it should be
integrate x^2 sin^2(x) instead of x^2 sin(x^2)

How did u guys type the sign of integral

 

[bomba923]

$$\int {x^2 \sin ^2 x\,dx}$$
can be evaluated via integration by parts.

jacy, the integral sign is just \int when using LaTeX.
Try clicking on this integral sign: $$\int$$

 

[jacy]

$$\int {x^2 \sin ^2 x\,dx}$$
can be evaluated via integration by parts.

jacy, the integral sign is just \int when using LaTeX.
Try clicking on this integral sign: $$\int$$

Thanks, yea now i can solve it