Integration by Trigonometric Substitution

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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 […]

Integration by Partial Fraction

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Integration by Partial Fraction If the function that need to be integrated is in the form of an algebraic fraction which is not easy to evaluate then you need to write the fraction into partial fraction to make it simpler for integration. You have to remember that this method is done only if the degree […]