TITLE: Beautiful Indefinite Integrals.
QUESTION [13 upvotes]: These are some of the integrals with beautiful solutions I came across-
$$\int \frac{x^2}{(x\sin x+\cos x)^2} dx$$
$$\int\frac {1}{\sin^3x+\cos^3x} dx$$
$$\int \frac{1}{x^4+1}dx$$
I'd love if you share some of the ones you came across.

REPLY [2 votes]: The Gaussian integral isn't indefinite but its derivation and answer are still remarkable:
$$\int_{-\infty}^{+\infty} e^{-x^2}\,dx = \sqrt{\pi}$$