$$\int\limits_{}^{} (6x-11 / x+2) dx$$

Question

amistre64 · Answer

nice job with the equation writing skill...kudos ;)

amistre64 · Answer

frac{top}{bottom} makes a clean fraction

anonymous · Answer

You need to substitute x for x=u+2 and then solve (dx=du since d/dy of +2 is zero).

anonymous · Answer

Err... that's not d/dy of +2 but the derivative of +2

amistre64 · Answer

$$\frac{top}{australia}$$

amistre64 · Answer

$$\int \frac{6x-11}{x+2}dx$$

anonymous · Answer

thanks for the lesson in writing equations >:(

anonymous · Answer

Do you get what I wrote msunprecedented?

anonymous · Answer

no, i did not

amistre64 · Answer

lol....  I was impressed by your talent ...still am :)

amistre64 · Answer

do you want the integral of 3 seperate terms; or is what I posted a correct interpretation of it?

anonymous · Answer

no its correct
$$\int\limits_{}^{} \frac {6x-11} {x+2} dx$$

amistre64 · Answer

... factoring might be possible but we would have to find out what value had been canceled before hand.... and then do partial decomposition as a possibility

anonymous · Answer

Actually, this is really simple if you view the fraction like this: $$6x/(x+2) - (11/x+2)$$ Now that it's in this form, you split the integral into two :
$$\int\limits_{?}^{?}6x/(x+2)dx - \int\limits_{?}^{?}11/(6x+2)dx$$
This should be easier to integrate... let me know if you need more help

amistre64 · Answer

the left is easy now :)  the right still has a straggler.... that "x" up top can get bothersome

amistre64 · Answer

and by left I mean right  ;)

amistre64 · Answer

would the uv substitution work well there?

anonymous · Answer

uv substitution wouldn't work because I don't think you could factor x+2. (I can't see a way to factor anyway)

amistre64 · Answer

6x goes to zero pretty quick like; but I get ln(x+2) and get lost on integrateing that

amistre64 · Answer

attachment

anonymous · Answer

Hmm.. I think integration by substitution works here. If you let u=x+2, you can get the right equal to:$$\int\limits_{?}^{?} (6u-12)/u *du$$
Then you split the fraction one more time

anonymous · Answer

I mean the left when I say the "right" above

amistre64 · Answer

lol..... stage left ...STAGE left!! :)

anonymous · Answer

Yikes! I'm soo confused! U-sub here? Integration by parts there? :(

anonymous · Answer

msunprecedented, have you learnt how to do integration by substitution yet?

anonymous · Answer

I believe not.