• TOC
  • Courses
  • Blog
  • Twitch
  • Shop
  • Search
    • Courses
    • Blog
    • Subreddit
    • Discord
    • Log in
    • Sign up
    • ▾Calculus 2
      • ▾Integration techniques
        • •Intro to calc 2
        • ▾Basic indefinite integrals
          • •Reverse power rule for indefinite integrals
          • •Sum, difference, and reverse power rules for indefinite integrals
        • •Integration by parts
        • ▸Integrals involving trig functions
          • •Lesson
          • •Practice
        • •Trig substitutions
        • •Integration by partial fractions
        • •Integral recurrence relations
        • •Integrating quadratics by completing the square
        • •Integration by long division
        • •Improper integrals
        • •Comparison tests for convergence
        • ▸Approximating definite integrals
          • •Riemann sums
          • ▸Simpson's rule
            • •Practice: Simpson's rule
          • ▸Trapezoidal rule
            • •Lesson
            • •Practice
          • •Midpoint rule
      • ▸Applications of integrals
        • ▸Arc length (calculus 2)
          • •Using the formula
        • ▸Center of mass (calculus 2)
          • •Center of mass for one and two-dimensional systems
          • •Center of mass for planar lamina
          • •Pappus's theorem
        • •Hydrostatic force
        • •Mode of a continuous random variable from a probability density function
        • •Surface area of solids of revolution
        • •Gabriel's Horn
        • •Applications of trigonometric integrals
        • •Integrating exponential functions
        • •Logarithmic functions
      • ▸Parametric equations and polar coordinates
        • •Cycloid area and length
        • •Eliminating the parameter
        • •Testing polar equations for symmetry
        • •Deriving the equations of a cycloid, epicycloid, and hypocycloid
      • ▸Series and sequences
        • •Maclaurin series
        • •Finding the sum of a telescoping series
        • ▸Convergent and divergent geometric series
          • •Lesson
          • •Practice
        • •Alternating harmonic series
        • •Alternating series test
        • •Partial sums
        • •Ratio test
        • ▸Root test
          • •Lesson
          • •Practice
        • •Absolute convergence, conditional convergence, and divergence
        • •Riemann's rearrangement theorem
        • •Taylor series
      • ▸Vectors
        • •Intro to vectors
        • •Length of a vector
        • •Cross product
        • •Intro to the dot product
      • •Competition problems (calculus 2)
     › Calculus 2 › Integration techniques › Basic indefinite integrals

    Reverse power rule for indefinite integrals

    \(\displaystyle\int x^3\ dx\)
    \(\dfrac{1}{4}x^4 + C\)
    2589Calculus 2: The Right Way to Think About Integration Technique (Integral of x³ by the Power Law)
    MathTheBeautiful
    \(\displaystyle \int x^5\,dx\)
    \(\dfrac{1}{6}x^6 + C\)
    171Reverse power rule
    Khan Academy ~ YouTube
    27494.1 Antiderivative Power Rule
    rootmath
    \(\displaystyle\int 3x^7\ dx\)
    \(\dfrac{3}{8}x^8 + C\)
    2590Calculus 2: Integral of 3x⁷ by the Power Law
    MathTheBeautiful
    \(\displaystyle \int 5x^{-2}\,dx\)
    \(-5x^{-1} + C\)
    171Reverse power rule
    Khan Academy ~ YouTube
    \(\displaystyle\int x^{-3 / 7}\ dx\)
    \(\dfrac{7}{4}x^{4 / 7} + C\)
    2591Calculus 2: The Integral of a Negative Exponent by the Power Law
    MathTheBeautiful
    \(\displaystyle\int x^{-3 / 7}\ dx\)

    Khan Academy videos

    • 171Reverse power rule
      Khan Academy ~ YouTube