WebDec 21, 2024 · A trigonometric function of a high power can be systematically reduced to trigonometric functions of lower powers until all antiderivatives can be computed. The … Web(Now use trig identity A from the beginning of this section.) (Use antiderivative rule 2 from the beginning of this section on the first integral.) . Now use u-substitution. Let so that , or . Substitute into the original problem, replacing all forms of , getting . Click HERE to return to the list of problems. SOLUTION 8 : Integrate . Use u ...
Integration techniques Calculus 2 Math Khan Academy
The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving … See more $${\displaystyle \int \sin ax\,dx=-{\frac {1}{a}}\cos ax+C}$$ $${\displaystyle \int \sin ^{2}{ax}\,dx={\frac {x}{2}}-{\frac {1}{4a}}\sin 2ax+C={\frac {x}{2}}-{\frac {1}{2a}}\sin ax\cos ax+C}$$ See more $${\displaystyle \int \cos ax\,dx={\frac {1}{a}}\sin ax+C}$$ $${\displaystyle \int \cos ^{2}{ax}\,dx={\frac {x}{2}}+{\frac {1}{4a}}\sin 2ax+C={\frac {x}{2}}+{\frac {1}{2a}}\sin ax\cos ax+C}$$ See more $${\displaystyle \int \csc ^{2}{x}\,dx=-\cot {x}+C}$$ See more An integral that is a rational function of the sine and cosine can be evaluated using Bioche's rules. $${\displaystyle \int {\frac {dx}{\cos ax\pm \sin ax}}={\frac {1}{a{\sqrt {2}}}}\ln \left \tan \left({\frac {ax}{2}}\pm {\frac {\pi }{8}}\right)\right +C}$$ See more $${\displaystyle \int \tan ax\,dx=-{\frac {1}{a}}\ln \cos ax +C={\frac {1}{a}}\ln \sec ax +C}$$ See more See Integral of the secant function. $${\displaystyle \int \sec ^{2}{x}\,dx=\tan {x}+C}$$ See more $${\displaystyle \int \cot ax\,dx={\frac {1}{a}}\ln \sin ax +C}$$ $${\displaystyle \int \cot ^{2}{x}\,dx=-\cot {x}-x+C}$$ See more WebList of Integral Formulas The list of basic integral formulas are ∫ 1 dx = x + C ∫ a dx = ax+ C ∫ x n dx = ( (x n+1 )/ (n+1))+C ; n≠1 ∫ sin x dx = – cos x + C ∫ cos x dx = sin x + C ∫ sec 2 x dx = tan x + C ∫ csc 2 x dx = -cot x + C ∫ sec x (tan x) dx = sec x + C ∫ csc x ( cot x) dx = – csc x + C ∫ (1/x) dx = ln x + C ∫ e x dx = e x + C la handidanse
6.3: Trigonometric Integrals - Mathematics LibreTexts
WebIntroduction to trigonometric substitution. Substitution with x=sin (theta) More trig sub practice. Trig and u substitution together (part 1) Trig and u substitution together (part 2) … Weball those angles for which functions are defined. The equation sin à = cos à is a trigonometric equation but not a trigonometric identity because it doesn [t hold for all values of àä There are some fundamental trigonometric identities which are used to prove further complex identities. Here is a list of all basic identities and formulas. lah and ester