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Exercise

$\int\left(x^2+5\right)e^{-3x}dx$

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Final answer to the exercise

$\frac{1}{-3}e^{-3x}x^2+\frac{1}{3}e^{-3x}-\frac{2}{9}xe^{-3x}+C_0$

Try other ways to solve this exercise

  • Choose an option
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Main Topic: Tabular Integration

Tabular integration is a special technique to solve certain integrals by parts usually made up of two functions: one polynomial and the other transcendent, like the exponential function or the sine. The method consists of deriving the polynomial function several times (until it becomes zero), and integrating the transcendent function several times. This method is usually applied when both functions can be easily derived and integrated multiple times.

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