Untitled Flashcards Set

∫ k dx | kx + C

∫ f(x) + g(x) dx | ∫ f(x) dx + ∫ g(x) dx

∫ c f(x) dx | c ∫ f(x) dx

∫ xⁿ dx | (xⁿ⁺¹) / (n+1) + C, n ≠ -1

∫ 1/x dx | ln|x| + C

∫ e^x dx | e^x + C

∫ a^x dx | (a^x) / (ln a) + C

∫ sin(x) dx | -cos(x) + C

∫ cos(x) dx | sin(x) + C

∫ sec²(x) dx | tan(x) + C

∫ csc²(x) dx | -cot(x) + C

∫ sec(x)tan(x) dx | sec(x) + C

∫ csc(x)cot(x) dx | -csc(x) + C

∫ 1/√(1-x²) dx | arcsin(x) + C

∫ 1/(1+x²) dx | arctan(x) + C

∫ 1/(x√(x²-1)) dx | arcsec(x) + C

Fundamental Theorem of Calculus (Part I): d/dx ∫ f(t) dt from a to x | f(x)

Fundamental Theorem of Calculus (Part II): ∫ f(x) dx from a to b | F(b) - F(a)

∫ e^(kx) dx | (1/k) e^(kx) + C, k ≠ 0

∫ sin(kx) dx | -(1/k) cos(kx) + C, k ≠ 0

∫ cos(kx) dx | (1/k) sin(kx) + C, k ≠ 0