Integrals of √(a²±x²) and √(x²-a²)

∫√(a²+x²)dx = (1/2) x√(a²+x²) + (1/2) a²log |x+ √(a²+x²)| +C

∫√(a²-x²) = (1/2) x√(a²-x²) + (1/2) a²sin^-1(x/a) + C

∫√(x²-a²) = (1/2) x√(x²-a²)- (1/2) a²log |x+ √(x²-a²)| +C