One of the coolest properties in integration not mentioned in any textbook I own. Try these:
1) Integrate: $$\int_{0}^{\pi/2}\frac{sin^{n}x}{sin^{n}x+cos^{n}x}\ dx\text{, for any integer }n$$
2) Integrate: $$\int_{0}^{\pi/2}\frac{1}{1+(tanx)^{\pi}}\ dx$$
3) Integrate: $$\int_{0}^{1}\frac{ln(x+1)}{x^{2}+1}\ dx$$
Yes, you need the answers and discussion HERE.