5

5+5 ffxe Zx 2X 5t5 X5 e (C FC 5 2x5545 @ ezx6+5_ zx S+5 30 € +C % exS+s+ c...

Question

5+5 ffxe Zx 2X 5t5 X5 e (C FC 5 2x5545 @ ezx6+5_ zx S+5 30 € +C % exS+s+ c

5+5 ffxe Zx 2X 5t5 X5 e (C FC 5 2x5545 @ ezx6+5_ zx S+5 30 € +C % exS+s+ c



Answers

$$\int \frac{10 x+2}{x^{3}-5 x^{2}+x-5} d x ; \text { use } \frac{A}{x-5}+\frac{B x+C}{x^{2}+1}$$

So 693 Problem Number 39 We're presented with an indefinite integral X sign of five X, and they give us a multitude of five choices of what this could be. Rather than write down all the choices, let's just go and work this through the integration by parts you is equal to X. Therefore, d'you is equal to T X, and then Devi is equal to sign of five x d. X. Therefore, V is equal to um minus co sign five X or minus one fifth so minus 1/5 uh, co sign of five x So this integral that you see here then becomes the integral of X sign of five x d. X is going to be equal to u V. So that's going to be minus X over five co sign of five X and then minus the integral of VD you So that's gonna be plus 1/5 and integral of VD you It's just gonna be co sign of five X. And so when you integrate that, your final answer is gonna be what minus x over five co sign of five x plus one over 25 sign of five X and then plus some integration constant. And then if you go back and look at the choices that they give you, this is straight out of choice number. Be okay. So in your choice, in your list of all the choices, this is exactly what shows up.

And some people here we are now solve this heavy houses coming up to be I quote be happier commodity two extra part 12 plus five extra nine bills or do I buy you just are probably real extra power fired about the problems that we have? Right then we have one plus one over X. Script calls didn't one of the extra parts find all kids must be a border. So now I just all this we have someone to be this divide by this summer to over we have execute supposed to be up five or we have extra politics bigger than politics here and we're divided by one plus one. Our expert Posted one over extra bar five then. Okay as we get here now if you just follow this little have here equals one plus one over X squared plus one of our extra part five P did he have been a good is coming activity negative two our Actually we have and then negative five forward extra ball six. Did you feel about here now? So this is finite amount of tv. You're having absence TX so immediately here so we get it asked negative beauty. No it's fine. Or we have thank you. So that's coming out to be negative due to the park negative three plus one over negative three plus one plus the So tonight is all this we get now 1/2. Then we have times one over the square plus the now this is told that that we have 1/2 times so and it does and one over these were so do we have taken he put one plus one over X. Squared plus one. Would like to point store one plus one over X squared plus one over after qualifying hospital plastic. That's got to be 1/2 times. We have The calcium here so. And is about to explode part 10. Or we have about five for the next few black one. Software platinum. So with your name on the record auction see we have extra part 10 over to mr part five for the S. Two plus one. Whole good. Love the record with you. Thank you.

Disintegrate handsomely computed by doing five F Thanks. Thanks. Blessed into government, you to five. Far the X This one we know it doesn't get you 18 as given here on Blessed. You continue for outside and we have angst. A Pirated from 2 to 5. So if we go to 18 plus from above, limit Manus, turn our image. So we should get 18 Blast for times 3 18 plus Trump, could you 30 day for the answer for this one to me when you go to a

We can use u substitution. We can set you equal to three X squared X. That's what the exponents is. Do you have a derivative? Is six acts DX Now we can set 1/6 d'you equal to x d axe. Therefore, we can write the integral as a number seven over six. On the outside, it's a constant. Remember the integral of each of the U. S. Just eat of the U giving us 7 62 the U Plus C And don't forget the last step is to substitute back in to 7/6 seed to the remember US three x squared plus C.


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