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Exercise

$5\int x^{-7}dx$

Step-by-step Solution

1

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $-7$

$5\left(\frac{x^{-6}}{-6}\right)$
2

Simplify the fraction $5\left(\frac{x^{-6}}{-6}\right)$

$-\frac{5}{6}x^{-6}$
3

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$-\frac{5}{6}x^{-6}+C_0$

Final answer to the exercise

$-\frac{5}{6}x^{-6}+C_0$

Try other ways to solve this exercise

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  • Integrate by partial fractions
  • Integrate by substitution
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  • 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: Integrals of Polynomial Functions

Integrals of polynomial functions.

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