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Point) Let5/12 tan6 (2x) sec(2x) dx:Express the value of3{12 tan8 ' (2x) sec(2x) dxin terms of [412 tan8 (2x) sec(2x) dx...

Question

Point) Let5/12 tan6 (2x) sec(2x) dx:Express the value of3{12 tan8 ' (2x) sec(2x) dxin terms of [412 tan8 (2x) sec(2x) dx

point) Let 5/12 tan6 (2x) sec(2x) dx: Express the value of 3{12 tan8 ' (2x) sec(2x) dx in terms of [ 412 tan8 (2x) sec(2x) dx



Answers

Evaluate the following integrals. $$\int \frac{2}{x^{2}-4 x-32} d x$$

Again this question were able to find out the solution of integration. 12 X squared, minus four whole days, five x dx and the limited to upper limit is three. Okay, so to solve this, uh, you can see student, we cannot solid directly. What? We have to apply the integration by substitution here, and we will substitute u equals two X squared, minus four. Okay. And it will give us the U equals to two x dx. Or we can say, Do you buy two Will be X dx. Okay. And why we have done this? Because we have X dx in our question. Okay. And this will be you raised to the power five. So before proceeding, we have to find out the new limits here for the lower limit. X Sequester two is given, and we have taken u equals two x squared minus or And when we put X sequester to hear it will be request to zero. That will be our new Yeah, lower limit. Okay. And now for the parliament for X is given three and we have taken you reconstruct square minus four. And when we put X equals to three here, it will be three square minus four. That is nine minus four. And that is five. It is our new a parliament. Okay. And now our question look like integration. Lower limit zero and a parliament five. Okay. And 12 and x squared, minus four. Raised to the power five, it will be you raised to the power five and x dx From here, it will be bu divided by two. Okay. And now we have to solve this. And it will be, uh, well divided by two. It will be six that will constant and 0 to 5 You raised to the power five and deal. Okay. Now six and integration of you raised to the power five d, you will be you raised to the power six divided by six. Okay. And the limited 0 to 5. And this six will cut this six. And it will be you raised to the power six and limited 0 to 5. And the student can we know down then. This is the limit for you. Okay, Not for X, so we will not back substitute here. You equal strength experiments, for we will directly apply the limits because because we have the limits for you, Not for X. So here. When applying the limit up limit minus lower limit. It will be five raised to the power six minus zero. Raise to the power six. Or of course, it will be five raised to the power six. Answer. And when we saw it, it will be 15,625. And that will be our final answer. Thank you.

This time, ask that they be integral of the rational function. 12 X men, etc. All Greg's to the Worth minus Teoh Squirt Bus one dear. Well, partial fractions tells us that it's from England. You have to repeated roots and X minus one X plus one. Something truly right. Your form properly, but we'll end up with negative to over. Plus one minus five over X plus ones. Word plus two over X minus one plus one over X minus one was quick. Okay, so this is actually just the raw. That's with positive terms for X minus one square. Honest to over. Expose one minus five. Overexpose one's quite yet. I don't fancy the ribs of those are pretty sure bar. We're gonna have a natural. We have civilian. Oh, that's my ones over X plus one squared. Like that. Time listing on this one. Yeah. And now, let's see. So the minus one over X minus one plus fine over X plus one was an arbitrary constants E

We have to find the value of the definite integral. That is even in the question. So four months ago square we will substitute by you. So money's of two X. Of the X equals to do you. Okay so two weeks of DX because two months of do you four months access code that is U to the power of three and 12 works dears we can add it minus of six. Do you? And when the limit is -1 When access management you will be four months 1 that is three when access managed to then you will be the limit will be four months 4. That is the cost to zero Months of six. Integration of this will be used to the about 414 minus of six. You to develop four of 14 The Limited 0- three. Okay So -6 of 14. Now we'll put celibate. So this will be a cost 23 to the power four mona's zero. So this will be close to minus six upon four In 2, 3 to the power forest 81. So It will be customers three. Why 2 in 281, 81 into three Will be to 43. So it will be Monakhov 2 43 upon two. So this is the Yeah answer. I hope you understood. Thank you.

They want to get the integral, uh, exquisite First while that minus 40. Over. Excuse mine. That's for it yet. And what if we do partial fraction decomposition on this rational function? We'll end up with one over X minus three over X plus two plus three over X minus two. So we're actually taking the interval. Uh, but see, one of the wrecks my street over expressed clustering over X man. It's too. Yes. Uh, I will give us natural. Look, uh, let's see. You can collect the money. Thanks. Times X minus two with metre log properties. Divide by explodes to give also with better luck properties. And I need that, and I'm a trade constancy.


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