Problem - 4620
Compute $$\int x^3\ln{x}d{x}$$
$$\int x^3\ln{x}d{x}=\frac{1}{4}\int\ln{x}d{x^4}=\frac{1}{4}\left(x^4\ln{x}-\int x^4d{(\ln{x})}\right)=\frac{1}{4}\left(x^4\ln{x}-\int x^3d{x}\right)=\boxed{\frac{1}{4}x^4\ln{x}-\frac{1}{16}x^4+C}$$
Compute $$\int x^3\ln{x}d{x}$$
$$\int x^3\ln{x}d{x}=\frac{1}{4}\int\ln{x}d{x^4}=\frac{1}{4}\left(x^4\ln{x}-\int x^4d{(\ln{x})}\right)=\frac{1}{4}\left(x^4\ln{x}-\int x^3d{x}\right)=\boxed{\frac{1}{4}x^4\ln{x}-\frac{1}{16}x^4+C}$$