Integral Substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) Definite Integrals Rules Definite Integral Boundaries

Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 11/2/2022 7:21:57 AM

Integral is called convergent if the limit exists and has a finite value and divergent if the limit doesn’t exist or has infinite value. This is typically a Calc II topic.

Indefinite Integrals Rules: ∫Integration By Parts: ′= −∫ ′ ∫Integral of a Constant: ( ) 𝑥=𝑥⋅ ( ) ∫Taking a Constant out: ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫Sum/Difference Rule: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥

1. Common Integrals. 2. Integrals of Rational Functions. 4. Integrals of Logarithmic Functions. 2 ! i ⋅ i ! 5. Integrals of Trig. Functions.

Trig Integrals: Integrals involving sin(x) and cos(x): Integrals involving sec(x) and tan(x): 1. If the power of the sine is odd and positive: Goal: ux cos i. Save a du x dx sin( ) ii. Convert the remaining factors to cos( )x (using sin 1 cos22x x.) 1.

Cheat Sheet for Integrals 1. u-Substitution For u-substitution, we usually look for a function (which we substitute as u), whose derivative is also present there. For example if the integrand (the function to be integrated) is cos3 xsinx, then the derivative of cosxwhich is sinxis also present (ignore that \ " as it is just the constant -1). So,

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