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Numerade Educator



Problem 53 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int x^2 \sinh mx\ dx $


$$\frac{1}{m} x^{2} \cosh (m x)-\frac{2}{m^{2}} x \sinh (m x)+\frac{2}{m^{3}} \cosh (m x)+C$$


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Video Transcript

Let's solve this one by using immigration by Earth's and let's take you to be X squared so that do you two x t x and then we're left over with Devi is the sign age. It's a hyperbolic sign and then the the anti derivative of this will be positive, not negative, hyperbolic co sign and then divided by m. So let's go ahead and use our formula here for my part so that you times v wow and then minus integral. And then we have V into you. So it's good and pull up this too in the m and then here let's go ahead and write that in. So that's Excuse me, will you take a step back here? So this is video and then we pulled out there too in the am. So now we have one more integral Let's do very similar buy parts again and we're almost finished here this time you x to use the X and then Devi hyperbolic co sign right so that he hyperbolic sign over him. So now you sing it again the same formula here, So don't forget it to over him in the front. And then we use the formula again. So you ve So this is our UV right here and then minus in a girl. And then we have VDO. I was going to pull up that him and in DX. So here, The last thing to do is to evaluate this. We already did this before. Let's going from here to here. And then don't forget that Theseus, who minuses will turn into a plus. So going on to the next page, let's write that final answer and then the double negative truths into a plus. And then here we will have three m's. So that will give us that I'm cute and then plus our constant denigration, see? And that's your final answer.