Question

what is the integral (x/(x+4) )dx ????/

Answer 1

what if we try to let u=x+4 => du=dx
if u=x+4 => x=u-4
\[\int\limits_{}^{}\frac{u-4}{u} du=\int\limits_{}^{}(1-\frac{4}{u}) du=u-4\ln|u|+C=(x+4)-4\ln|x+4|+C\]

Answer 2

check: take derivative of antiderivative
(1+0)-4*1/(x+4)+0

1-4/(x+4)

[(x+4)-4]/(x+4)

x/(x+4)

so yay!

answer checks out! :)

Answer 3

um no u is X to the power of 4 :(

Answer 4

what?

Answer 5

we have
\[\int\limits_{}^{}\frac{x}{x+4} dx=(x+4)-4\ln|x+4|+C\]

Answer 6

this is totally correct unless you made a mistake in your question

Answer 7

what is the integral (x/(1+x^4))dx