### Integration by Trigonometric Substitution

Integration by Trigonometric Substitution 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 […]