Integration Rules and Techniques - Grove City College

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. sinh(x) dx = cosh(x) + C. csch(x) coth(x) dx = csch(x) + C. Z Z. cosh(x) dx = sinh(x) + C sech(x) tanh(x) dx = sech(x) + C.

1. Logarithmic 2. Inverse Trigonometric 3. Algebraic, such as polynomials (including powers of x) and rational functions. 4. Trigonometric 5. Exponential and then whatever is left is dv. This doesn’t always work, but it’s a good place to start. With de nite integrals, the formula becomes Z b a udv= u(x)v(x)]b a Z b a vdu:

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  Rules, Technique, Integration, Logarithmic, Exponential, Integration rules and techniques

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