can someone help me with this integral ? ∫6x^3/(2x^4+1)

Question

amistre64 · Answer

the top is almost a derivative of the bottom ... what is the derivative of the bottom?

amistre64 · Answer

also, recall derivative of ln(u) to see why thats one of the first things you try to look at.

anonymous · Answer

attachment

anonymous · Answer

i don't get where the 3/4  comes from...

amistre64 · Answer

what is the derivative of the bottom?

amistre64 · Answer

what is the deriative of:  2x^4 + 1

anonymous · Answer

8x^3

amistre64 · Answer

good, then we would be sitting pretty if the top was 8x^3,  but it aint, so we need to use some math to transform it into an 8

amistre64 · Answer

do you agree that 8/8 = 1?

anonymous · Answer

lol yes

amistre64 · Answer

$$\int\frac{6x^3}{2x^4+1}$$
pull out the 6 and multiply it all by 8/8, why?
$$6\int\frac{8}{8}\frac{x^3}{2x^4+1}$$
use the top 8 and pull the bottom 8 out of the way
$$\frac 68\int\frac{8x^3}{2x^4+1}$$
etc ...

amistre64 · Answer

now we integrate it up into:  6/8  ln(2x^4+1) + C

anonymous · Answer

awesome! thank you!

amistre64 · Answer

youre welcome