5

10 Find the indefinite integral | 1tan u +18 dii A) Itanu + 7u+C Htanu +9u+C 8 Htanu - Tu+C 11 tan' u + 18u +€ ; E) ALtan' u+18u+C...

Question

10 Find the indefinite integral | 1tan u +18 dii A) Itanu + 7u+C Htanu +9u+C 8 Htanu - Tu+C 11 tan' u + 18u +€ ; E) ALtan' u+18u+C

10 Find the indefinite integral | 1tan u +18 dii A) Itanu + 7u+C Htanu +9u+C 8 Htanu - Tu+C 11 tan' u + 18u +€ ; E) ALtan' u+18u+C



Answers

In Exercises $7-24,$ write the integral in terms of $u$ and $d u$ Then evaluate.
$$\int\left(\sec ^{2} t\right) e^{\tan t} d t, \quad u=\tan t$$

Okay. Were given a square root. Let me start that start in a room of sequence squared T and each of the changes of tea dpt It was legal to change into things. So you and therefore sequins were g d g. But has she could go? Did you over here and here that people to get to you pageant thi is this you Do we get Mmm, Either you do you taking in a row that we just get each of you plus seeing replacing are you will get me to the changes G C.

Whether given integral will make that substitution cage quarto one minus u to the power you so different sitting gold cells will have the cage fall to minus You talk about you, do you? So my next day again, this photo into the power you do you the given in Dingle becomes minus. What do you make it like? A square which is part of minus my next one. Like it glassy, which is all toe on my care policy. Starting back. I'm an issue. Let's see, she's not find an answer.

For the Given Kush integration we have now multiply negative totems will have to your squared plus nine you less food, do you? Which is a quarto And it isn't two years could all be too. And you open the power to plus one. Wondered about two plus one last nine. And to help the power one plus one help one plus one that's four in tow. The power one. So let's see that will make Porto My three used the power three last nine by two. You squared less for you. Let's see. Let's see the hospital 20 lesson.

20. We need to complete this. We need to convert this complete integrate in terms off you and do you using this substitution? So let's differentiate both sides. So do you. Comes as differentiation off tennis Sex Square X and D extreme means other players. So the integrate consult us 10 x is replaced by you on over here Sex square X times dx from the situation is replaced Where d so we have to you over here. So the integrate comes orders you square over two plus See where u s Dan X The integration is used for over over two plus See where u s tannic. So finally, if you replace you by tonics we're getting 10 square X who were toe plus c So this is the final line.


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