/sci/ - Science & Math

[Anonymous No.7248140]

I have a question about about integrals and fractions
mianly, I haven't done calc in a long time and I forget some of the fraction/power rules

So if i have u/(1/3(du)^3) dx
to bring du to the top what changes? would it be u multiplied by 3 du^-3??

[OP No.7248143]

and before someone says "take your homework somewhere else"
this isn't homework, i'm actually trying to teach myself integral calc on my own so that I can understand a physics course better that I plan to take in the future

[OP No.7248145]

I'm doing u-substitution, for the most part i understand it but im having a hard time of what to do next after i've picked my u and found the derivative of my u (i.e. the du)

[Anonymous No.7248148]

Post the original problem

[Anonymous No.7248152]

>>7248145
>>7248148
This, you probably fucked up the u-substitution somehow.

[OP No.7248170]

original problem

integral (1+ sin x)/ cos^2 x dx

[OP No.7248174]

>>7248170

I let my u= 1+ sin x because it's derivative appears in the function... cos x
i rewrote cos^2 x as (cos x)^2

[Anonymous No.7248178]

>>7248174
Wrong way.

1/cos2=sec2-> tan

sin/cos^2->(-1/3)cos^-3

[Anonymous No.7248182]

Use trig identities and then u sub

[Anonymous No.7248185]

>>7248178
nvm

-1cos^-1

[Anonymous No.7248188]

>>7248174
btw you can't write cos^2(x) as (cos x)^2

[Anonymous No.7248194]

>>7248188
Yes you can.

http://www.wolframalpha.com/input/?i=cos%28x%29^2

[Anonymous No.7248200]

>>7248194
yeah nevermind i checked it and i thought the x would also square

[OP No.7248212]

>>7248178

So you're saying i can rewrite this integrand as
integral 1/cos x + -sin x/ cos x dx

[Anonymous No.7248215]

>>7248212
What no

1/cos^2 + sin/cos^2

[Anonymous No.7248223]

>>7248215
Then rewrite this as sec^2(x) + tan(x)sec(x). If you memorize the derivatives of trig functions you should be able to take it from here

[Anonymous No.7248226]

>>7248223
yes the problem is pretty much finished after this

[OP No.7248297]

So
integral (sec x)^2 + (tan x)(sec x) dx
u= tan x
du= (sec x)^2 dx
and then sub back in so,
integral u(sec x) du

[Anonymous No.7248298]

>>7248297
nuuuuuu

what are you doing

you don't need to u-sub at all

[Anonymous No.7249945]

(1+sinx)/(cos2x)dx=
=(1+sinx)/(1-sin2x)dx=
=(1+sinx)/((1+sinx)(1-sinx))dx=
=1/(1-sinx)dx

[Anonymous No.7250003]

NO OP PLS, no subs are needed