Calc II...

[maldecido33 10+ year member]

MathCAD is your best friend when it comes to checking answers/steps

 

[bk12321 10+ year member]

Alright I need some more help

I did this problem already, answer at the bottom, if somebody could check my work id appreciate it, I just wanna make sure its right for class tomorrow.

#6. Consider the indefinite integral: (integral) (4x^3+4x^2-27x-33)/(x^2+9) dx

The integrand decomposes into this form: ax + b + c/x-3 d/x+3

Ive gotta find a,b,c, and d, and then integrate using partial fractions to get the antiderivative of the entire integral you see above.

Using long division of x^2+9 into the big part, I get a remainder of 9x+3 and a quotient of 4x+4,

so now I have 4x + 4 + (integral) (9x+3)/(x^2+9) dx. much simpler integral.

partial fractions part:

9x+3/(x+3)(x-3)

therefore

(A(x-3)+B(x+3))/((x+3)(x-3))

again therefore

((A+B)x+(-3A+3B))/(x+3)(x-3)

using the equation I found from doing the long division... I know

A+B=9

-3A+3B=3

so 6b = 30 and B = 5

A=4

THEREFORE

(integral) (4x+4) dx + (integral) (5/x-3) dx + (integral) (4/x+3) dx =

2x^2 + 4x + (5)(ln(abs(x-3))) + (4)(ln(abs(x+3))) + C

is that right??? lol sorry I know its a pain to read typed out calc II

 

[its_bacon12 10+ year member]

**** calc 2.. i tried taking it 3 times in college and failed all 3 times..

the third time that would have been a fail i dropped it

 

[bk12321 10+ year member]

**** calc 2.. i tried taking it 3 times in college and failed all 3 times..
the third time that would have been a fail i dropped it

****.

did u get past integrals????

cuz that is kicking my ***, but i am getting it so far i guess

it just doesnt need to get much harder

 

[bk12321 10+ year member]

oh and ive got one more but ill type it out after someone helps me with this first one haha...

 

[ToyTundra 10+ year member]

THEREFORE

(integral) (4x+4) dx + (integral) (5/x-3) dx + (integral) (4/x+3) dx =

2x^2 + 4x + (5)(ln(abs(x-3))) + (4)(ln(abs(x+3))) + C

is that right??? lol sorry I know its a pain to read typed out calc II

looks right to me, but all i did was mental math

 

[bk12321 10+ year member]

looks right to me, but all i did was mental math

sounds good to me

i just wanted to know if it looked even close to right, and if i was doin the right thing

 

[PollyCranopolis 10+ year member]

wtf is a integral?

 

[hoxie08 5,000+ posts]

man i wish i could understand that..oh well

 

[bk12321 10+ year member]

wtf is a integral?

An integral is the area under a function f(x).

man i wish i could understand that..oh well

lol... i still have trouble understanding half of it.