Why aren't these two integration methods yielding the same answer? I'm trying to solve this (not homework, if it matters), and both u-substitution and integration by parts are both yielding two different answers. Where am I going wrong?
Equation: $$\int \frac{(4x^3)}{(x^4+7)}dx$$
u-substitution answer: $$=\ln\big|(x^4+7)\big|+C$$
integration by parts answer: 
$$=\int4x^3*(x^4+7)^{-1}dx$$
$$=4x^3*\ln\big|x^4+7\big|-\int 12x^2*(x^4+7)^{-1}dx$$
$$=4x^3*\ln\big|x^4+7\big|-(12x^2*ln\big|x^4+7\big|-\int 24x*(x^4+7)^{-1}dx)$$
$$=4x^3*\ln\big|x^4+7\big|-(12x^2*ln\big|x^4+7\big|-24x*ln\big|x^4+7\big|-\int 24(x^4+7)^{-1}dx)$$
$$= 4x^3*\ln\big|x^4+7\big|-(12x^2*\ln\big|x^4+7\big|-(24x\ln\big|x^4+7\big|-24\ln\big|x^4+7\big|))$$
$$=(4x^3-12x^2+24x-24)(\ln\big|x^4+7\big|)$$

The correct result is:
$$\int\frac{4x^3}{x^4+7}dx=\ln|x^4+7|+c$$.
With substitution: $u=x^4+7$ from which $du=4x^3dx$ hence the integral become:
$$\int\frac{du}{u}=\ln|u|+c$$.
Integration by parts it's not raccomanded in this case.
