### Integration by Trigonometric Substitution

Algebraic expressions Depending on the function we need to integrate, we can use this trigonometric expression as substitution to simplify the integral: 1. When $ displaystyle sqrt{{{{a}^{2}}-{{b}^{2}}{{x}^{2}}}}$ then substitute $ displaystyle x=frac{a}{b}sin theta $ and the helpful trigonometric identities is $ displaystyle {{sin }^{2}}x=1-{{cos }^{2}}x$ 2. When $ displaystyle sqrt{{{{a}^{2}}+{{b}^{2}}{{x}^{2}}}}$ then substitute $ displaystyle x=frac{a}{b}tan theta $ […]