Integration Rules and Techniques

Integration Rules and Techniques Antiderivatives of Basic Functions Power Rule (Complete). n+1. x Z . + C, if n 6= 1. n +1.. xn dx =.. ln |x| + C, if n = 1.. Exponential Functions With base a: ax Z. ax dx = +C. ln(a). With base e, this becomes: Z. ex dx = ex + C. If we have base e and a linear function in the exponent, then Z. 1. eax+b dx = eax+b + C. a Trigonometric Functions Z Z. sin(x) dx = cos(x) + C. cos(x) dx = sin(x) + C. Z Z. sec2 (x) dx = tan(x) + C csc2 (x) dx = cot(x) + C. Z Z. sec(x) tan(x) dx = sec(x) + C. csc(x) cot(x) dx = csc(x) + C. 1. Inverse Trigonometric Functions Z. 1. dx = arcsin(x) + C. 1 x2. Z. 1. dx = arcsec(x) + C. x x2 1. Z. 1. dx = arctan(x) + C. 1 + x2. More generally, Z. 1 1 x . dx = arctan +C. a2 + x2 a a Hyperbolic Functions Z Z.

For integrals involving only powers of sine and cosine (both with the same argument): If at least one of them is raised to an odd power, pull o one to save for a u-sub, use a Pythagorean identity (cos 2 (x) = 1 sin 2 (x) or sin 2 (x) = 1 cos 2 (x)) to convert the remaining (now even) power to

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  Rules, Technique, Integration, Sine, Isceon, Sine and cosine, Integration rules and techniques

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