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Evaluate the integral: 9r" 9r +9...

Question

Evaluate the integral: 9r" 9r +9

Evaluate the integral: 9r" 9r +9



Answers

Evaluate the given integral. $$\int \frac{x}{x^{2}+9} d x$$

Okay, so we're asked to find the anti derivative of the function DX over X, which is really the function is one over X, and we want that with respect to X from 1 to 9. And I pulled this up on my graphing calculator function I entered was one over X and what it's asking us to do is find the area of this shaded space. So we're gonna do that by reminding ourselves that there are anti derivatives rule for D. U. Over you is the natural log of the absolute value of you. Plus see, if I'm talking about a general anti derivative in this case, we know what our limits are. So we're talking about definite liberal. So in this case, since you is equal, the X I have no use substitution to worry about. So my anti derivative of DX over X will be natural log of absolute value of X plus C and our anti derivative. Our natural log of X, evaluated from nine down toe one, takes us to the natural log of absolute value of nine and that absolute values not necessary in this case because nine is positive minus natural log of one absolute value natural log of nine. Remember, I can drop the absolute value. Um, I would need a calculator to calculate that the natural log of one, even zero. Remember, this is E tow. What power equals one is a zero. So our final solution is natural log of nine on our calculator. Even though it's not a calculator question. If we want to find that anti derivative value, I have it up here. A second ago, the screen went away. Um, go back to that. I want the anti derivative with a lower limit of one and an upper limit of nine. So we're looking for looks when I lost it again. 2.9 is, I think, what it said. So, um, evaluating on my calculator, just to be sure that were accurate. My natural log of nine is 2.1 night. Excuse me. That's what it said. 2.19 so we know that's correct.

Even in a big girl Be it divided by order to square minus nine The power really way No. Hey, I'll accept you. It is going to do. Did he buy too? So we can simplify the express And in the NGV Nazi here how we can simplify Plastech derivative both sides deities who defy to I don't know the debate about set picked up. Did you wait? Accepted and dancing and meeting now Blood in the belly of your ex Andy It given in figure. So area get the place off the it 32 protected that in good at that and did it now according to relieve A to sick picked up in the Polish square minus nine in the power anyway, not simplify this expression. Then we'll get one by it be and do sidekick That divided right, Daniel Sweat. I think that now in the place off secretary weekend I One day after that and the place off Santa, we can write Santa Scott ETA divided way off the slight that now the top from the move Better And then they'll get one way a training room. Ortega If I didn't really sank it there in one by sand people. When the simplified is that person again will get drafted by science Now in the place off Santa Tablet Kakuta we can buy the place up Sanctum ricotta we can I or in the place of always Ancheta we can I force it into the vaginal integrates um off the core. Kitna in a car said that in bitter minus one but getting into miners while sitting down. Unless cc then integral want now like in the bellow off or second. So the video a positive that it will do well divided by gender. What? It was wet. My left name. Let's see what kinds of the from the numerator and denominator they get minus X divided by nine into Kendall Orica Square minus nine. Bless you. So this is the solution given in figure. Thank you.

The problem we have indication 4 to 5. One upon nine minus X. Squad. Dx know this can be written as one upon three plus X into three minus X. That is equal to a pond three plus X plus Be upon 3 -6 It is one equals 8: 3 -6 Plus B into three plus x. So these equals Equal to 1.6 and be equal to 1.6. Further this is written as integration 4-5 one upon 6 into three plus X Plus one About 6 into three -X. Dx. This is equal to 1.6. Ellen Model three Plus X Plus one About 6. Ellen Martin 3 -1 upon -1. 4- five days equals two. One about six Ln march three plus x -1 upon six. Ellen Mod 3 -1 Here. 4: five. Therefore further we have these equals two, one upon six and then mod -4 upon -7 that equals two 1.6. L. N. Mud four upon seven. This is really your pain after putting their limits. Hence we have, the answer is -0.093. So this is the answer.


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