Question

Using u sub find the integral of sin2x/1+cos^2x

Answer 1

@zepdrix

Answer 2

let 1+cos^2x = u

Answer 3

Okay

Answer 4

rest should be easy if you're familiar with the general method of substitution

Answer 5

Let me try it I'm not the best at it

Answer 6

I'll let you know what I get

Answer 7

sounds good

Answer 8

So wait when using u sub were trying to get sin2x right?

Answer 9

may i suggest you watch this awesome video on u substitution first
https://www.khanacademy.org/math/integral-calculus/integration-techniques/u-substitution/v/u-substitution

Answer 10

Okay

Answer 11

Okay I watched it that was pretty helpful :)

Answer 12

Okay I got ln|1+cos^2|+c?

Answer 13

@ganeshie8 @zepdrix is it right?. :D

Answer 14

Wait...its -ln

Answer 15

Ya that sounds better :o

Answer 16

The derivative of cosx is -sinx

Answer 17

Ughhhhhhh

Answer 18

How do you don't this one find the integral of x^2square root 2+x?

Answer 19

This?\[\large\rm \int\limits x^2\sqrt{2+x}~dx\]There is a little trick to it.

Answer 20

Yeah I put 2+x as my u I don't think that was a wise move

Answer 21

\[\large\rm u=2+x\]Now, before you go looking for your \(\large\rm du\),
let's modify this to create an x^2.

Answer 22

Subtracting 2,\[\large\rm u-2=x\]

Answer 23

Hmmm okay

Answer 24

Squaring,\[\large\rm (u-2)^2=x^2\]

Answer 25

To find your \(\large\rm du\),
use the original substitution that we set up.

Answer 26

Oh wow

Answer 27

Wait what

Answer 28

Your saying du=dx use the original one?

Answer 29

Good, that looks right.
So, this was a little trickier, ya?
We instead have `three pieces` to replace.

Answer 30

Yes

Answer 31

\[\rm \color{orangered}{u=2+x}\]\[\rm \color{royalblue}{(u-2)^2=x^2}\]\[\rm \color{green}{du=dx}\]Into our integral,\[\large\rm \int\limits \color{royalblue}{x^2}\sqrt{\color{orangered}{2+x}}~\color{green}{dx}\]

Answer 32

Woooo let me think this lol

Answer 33

So (u-2)^2times square root u du?

Answer 34

\[\large\rm \int\limits (u-2)^2u^{1/2}du\]Mmm k good.

Answer 35

No nice tricks from this point,
just expand out the square, multiply the u^{1/2} into each,
and integrate term by term, power rule.

Answer 36

Okay

Answer 37

Okay

Answer 38

U^5/2-2u^3/2+4u^1/2

Answer 39

woops, middle term is -4u^{3/2}

Answer 40

oh yeah oops :D

Answer 41

I was nervous I was like wait am I supposed to multiply exponents I always forget... not a good thing, so basic things I should probably be reviewing

Answer 42

So now take the integral of it you get

Answer 43

it wont let me use the equation thingy...dumb

Answer 44

twiddla? :d lol

Answer 45

what about it? you wanna go on there?

Answer 46

ya maybe :D if it wont let you use the equation tool

Answer 47

yeah lets do it

Answer 48

https://www.twiddla.com/mvbswa