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Basic and Trigonometric Integrals in Calculus

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Terms in this set (24)

  • Integral of \(u^n\) with respect to u, for n ≠ -1
    ∫u^n du = \(\frac{u^{n+1}}{n+1}\) + C
  • Integral of \(\frac{1}{u}\) with respect to u
    ∫(1/u) du = ln|u| + C
  • Integral of \(e^u\) with respect to u
    ∫e^u du = e^u + C
  • Integral of \(a^u\) with respect to u, a > 0, a ≠ 1
    ∫a^u du = \(\frac{a^u}{\ln a}\) + C
  • Integral of \(\sin u\) with respect to u
    ∫sin u du = -cos u + C
  • Integral of \(\cos u\) with respect to u
    ∫cos u du = sin u + C
  • Integral of \(\sec^2 u\) with respect to u
    ∫sec^2 u du = tan u + C
  • Integral of \(\csc^2 u\) with respect to u
    ∫csc^2 u du = -cot u + C
  • Integral of \(\sec u \tan u\) with respect to u
    ∫sec u tan u du = sec u + C
  • Integral of \(\csc u \cot u\) with respect to u
    ∫csc u cot u du = -csc u + C
  • Integral of \(\tan u\) with respect to u
    ∫tan u du = ln|sec u| + C
  • Integral of \(\cot u\) with respect to u
    ∫cot u du = ln|sin u| + C
  • Integral of \(\sec u\) with respect to u
    ∫sec u du = ln|sec u + tan u| + C
  • Integral of \(\csc u\) with respect to u
    ∫csc u du = ln|csc u - cot u| + C
  • Integral of \(\sin^2 u\) with respect to u
    ∫sin^2 u du = 1/2 u - 1/4 sin 2u + C
  • Integral of \(\cos^2 u\) with respect to u
    ∫cos^2 u du = 1/2 u + 1/4 sin 2u + C
  • Integral of \(\tan^2 u\) with respect to u
    ∫tan^2 u du = tan u - u + C
  • Integral of \(\cot^2 u\) with respect to u
    ∫cot^2 u du = -cot u - u + C
  • Integral of \(\sin^3 u\) with respect to u
    ∫sin^3 u du = -1/3 (2 + sin^2 u) cos u + C
  • Integral of \(\cos^3 u\) with respect to u
    ∫cos^3 u du = 1/3 (2 + cos^2 u) sin u + C
  • Integral of \(\tan^3 u\) with respect to u
    ∫tan^3 u du = 1/2 tan^2 u + ln|cos u| + C
  • Integral of \(\cot^3 u\) with respect to u
    ∫cot^3 u du = -1/2 cot^2 u - ln|sin u| + C
  • Integral of \(\sec^3 u\) with respect to u
    ∫sec^3 u du = 1/2 sec u tan u + 1/2 ln|sec u + tan u| + C
  • Integral of \(\csc^3 u\) with respect to u
    ∫csc^3 u du = -1/2 csc u cot u + 1/2 ln|csc u - cot u| + C