solve-the-given-problems-by-integration-find-an-equation-of-the-curve-that-passes-through-10-and-the

Question

Solve the given problems by integration.
Find an equation of the curve that passes through $(1,0),$ and the general expression for the slope is $(3 x+5) /\left(x^{2}+5 x\right)$

Linh Vu · Accepted Answer

calm down. Will you call that we have the new acts and then now an. And then we want to do the doing over the X for this one. Then we should get equal. Judah in terms. New act Bala on the an minus one. Then be over the eggs under your ex. So now in the question were given you will be the square, the square of the expert tree Bus five want you Don&#x27;t be over the X here by family, we can register into the expo to justify, um a half. Therefore, we&#x27;re gonna apply the formula again. And a half now and then we have the expert was five, but ah, half minus one. So get a minus, Have. And then by the general religion attempts the expert drinkers five million to so it doesn&#x27;t get ecology and a half and then expert through those five Obama and that&#x27;s a half the river. There is a Nico June the three x square. So from here, we can conclude that into go off the uh huh off the, uh, there&#x27;s only three out of you. And then we have, uh, thanks ground the top X about dribbles five square root here the X They were ego Judy inside here. So we&#x27;ll be squared on the expert tree was five. And don&#x27;t forget your blessed constancy here.

Aishwarya Krishnakumar · Answer

from 17 morass to use u substitution to find this indefinite integral. So we&#x27;re gonna let you equal the denominator, so you equals three. Plus I&#x27;ve x squared, and then we can go ahead and take the derivative of both sides. Do you equals and X T ads. And as you can see this, it&#x27;s the same thing as this. So you can rewrite this as the integral of won over you because issue shows up right here. Do you? The Sequels, Ellen of you see? But you can&#x27;t keep it in terms of you. So you have to begin three waas fried that squared. Let&#x27;s see. And this is the fact.

Runpeng Li · Answer

So, for a problem. 19 we need to find a slow off your function, which is flying equal to equals two. Uh, that&#x27;s why you cause five X minus three X squared. So we take the directive that gives five minus six X are plugging X X equals one. So that gives five minus six, which is selective one. And that is a slope off the

Foster Wisusik · Answer

Okay, This question wants us to find the anti derivative of this function. So let&#x27;s pick you to be equal to our function under the Cube root here because this tells us that D U is just equal to the ex. And then we also would like to get rid of this X plus five. Right now we just have X minus five. So to change that, let&#x27;s just add 10 double sides of are you equation? So we get you plus 10 equals X minus five plus 10 or X plus five. So now we can fully eliminate all the exes in the equation. So are integral becomes the integral of X plus five. And we said expose five is equal to you, plus 10 times you to the 1/3 d U hands. We could just distribute now and get you to the 3/3 plus 1/3 and then plus 10 you to the 1/3 d U. So now let&#x27;s just take these anti derivatives and get 3/7 you to the 7/3 plus 10 times 3/4 you to the 4/3 plus C or simplifying and plugging back in. We get 3/7 and then you was X minus five. Raise that to the seventh parents, and then we get 30/4, which reduces to 15 over too. So we get 15 over too Times X minus five to the 4/3 plus C.

Bobby Barnes · Answer

they want to verify this formula by using differentiation. So what we want to do is think the derivative of this function on the right hand side and see if we get what we are integrating here. So go ahead and apply are derivative to the right hand side. So derivative of negative three X plus five raised the negative 1/3 plus C. Now the derivative is a linear operator, so we can distribute it across the plus and minus as well as Paul. Any Constance. So we can rewrite this us negative 1/3 and then taking the integral of three x plus five recent negative first power is going to be power and changeable. So power rule, her says. We subtract one from Powers. There&#x27;s gonna be negative, too now and then we multiply with Clarence and different color negative, too, and we multiply by the whole powers that be negative one and then change Will says we have to take a trip of our inside function, and the derivative of three X plus five would just be three multiplied by three. And it would take the derivative of a constant. See, that&#x27;s just zero. Let&#x27;s go ahead and clean this up a little bit. So first thes negatives council out with each other and this three and that three councils out, so we would be left with three X plus five raise to the negative second power. And this is exactly what we were trying to integrate. So this is so that formula up there does hold.

Problem

The current $i$ (in $\mathrm{A}$ ) as a function …

Problem 33 Easy Difficulty

Solve the given problems by integration.
Find an equation of the curve that passes through $(1,0),$ and the general expression for the slope is $(3 x+5) /\left(x^{2}+5 x\right)$

Answer

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus