Integration

[random stream]

Can somebody tell me how to integrate this funcion pls? I thought it could be done by some substitution, but I have no idea how to do so...

[versed estuary]

use intergral of 1/x=lnx

[tight summit]

It’s such a trick u sub

$\sqrt{x+5}=u$

[sage anvil]

axkyn

[tight summit]

$u^2=x+5$

[sage anvil]

axkyn

[tight summit]

$U^2-5=x$

[sage anvil]

axkyn

[tight summit]

Take deravative

2udu=dx

$\int \frac{2u}{2+u}du$

[sage anvil]

axkyn

[tight summit]

And then use ibp

Wait no

Um

@random stream

[stiff mural]

$\int 2u(2+u)^{-1}du$

[sage anvil]

axkyn

[stiff mural]

Um

Actually I don’t think you solve it in this manner

[versed estuary]

2 outside becos constant

then write u as u+2-2?

does that work?

[stiff mural]

Yeah that’s what I was thinking idk

[versed estuary]

yeah that works

i got it

[stiff mural]

Yeah it definitely works

?? 2u is a variable it’s not a constant

[tulip topaz]

Oh shoot

My bad, let me fix that

This is new to me hold on

Oh but wait it’s a product

The integral, would you use integration by parts?

After the u-sub?

Let me try that

[stiff mural]

$2\int \frac{u}{u+2}du$

[sage anvil]

axkyn

[stiff mural]

$-4\int \frac{1}{u+2}du$

[sage anvil]

axkyn

[tulip topaz]

What did u do here?

[stiff mural]

$-4(ln|u+2|)+C$

[sage anvil]

axkyn

[stiff mural]

$\sqrt{x+5}=u$

[sage anvil]

axkyn

[stiff mural]

$-4(ln|\sqrt{x+5}+2}|)+C$

[sage anvil]

axkyn
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[stiff mural]

This is probably wrong

[tulip topaz]

Can u tell me how above, u went from a constant of 2 outside the integral to -4, and how the u for the numerator became a 1?

[stiff mural]

$2 \int \frac{u+2-2}{u+2}du$

[sage anvil]

axkyn

[stiff mural]

$2\int \frac{-2}{u+2}du$

[sage anvil]

axkyn

[stiff mural]

$-4 \int \frac{1}{u+2} du$

[sage anvil]

axkyn

[stiff mural]

Here

@tulip topaz

[stiff mural]

@versed estuary

[tulip topaz]

Ok that makes sense, thank you

[stiff mural]

No problem

You just starting integration?

[tulip topaz]

Yeah, it’s my first year of AP calc.

[stiff mural]

What’s your age

[tulip topaz]

17

I’m going into calc 2 September

[stiff mural]

Dang

[stiff mural]

Oh your older then me

[random stream]

Thanks now i got it!

I´m 19, first year in college. We´re having calc test on thursday.

[stiff mural]

Nice

[stiff mural]

You all are older than me

[stiff mural]

You got it

[glad burrow]

(u+2-2)/(u+2) = 1 - 2/(u+2)

[stiff mural]

Oh shi

Thanks

$2(u-2\int \frac{1}{u+2} du$

[sage anvil]

axkyn

[stiff mural]

$2u-4 ln|u+2|+C$

[sage anvil]

axkyn

[stiff mural]

@glad burrow silly mistake by me

[glad burrow]

It's fine just be careful

[stiff mural]

I was walking on a trail

[versed estuary]

yeah no thats wrong

[stiff mural]

Yeah ik