\(\displaystyle\int x^3\ dx\)
\(\dfrac{1}{4}x^4 + C\)

Calculus 2: The Right Way to Think About Integration Technique (Integral of x³ by the Power Law)
MathTheBeautiful
\(\displaystyle \int x^5\,dx\)
\(\dfrac{1}{6}x^6 + C\)
Reverse power rule
\(\displaystyle\int 3x^7\ dx\)
\(\dfrac{3}{8}x^8 + C\)

\(\displaystyle \int 5x^{-2}\,dx\)
\(-5x^{-1} + C\)
Reverse power rule
\(\displaystyle\int x^{-3 / 7}\ dx\)
\(\dfrac{7}{4}x^{4 / 7} + C\)

Calculus 2: The Integral of a Negative Exponent by the Power Law
MathTheBeautiful
\(\displaystyle\int x^{-3 / 7}\ dx\)