Power Rule of Integration
Posted: Fri Apr 17, 2026 3:24 pm
\(\int x^{n}\,\,dx = \dfrac{x^{n + 1}}{(n + 1)} + C \)
\(when\)
\(x \neq -1\)
\(and\)
\(C = any\,\,real\,\,number\)
\(ex\,\, a.\)
\(\int 5x^{3}\,\,dx = \dfrac{5x^{3 + 1}}{(3 + 1)}\,\,dx = \dfrac{5x^{4}}{4} + C \)
\(ex\,\, b.\)
\(\int 10x^{4}\,\,dx = \dfrac{10x^{4 + 1}}{(4 + 1)}\,\,dx = \dfrac{10x^{5}}{5} + C = 2x^{5} + C\)
\(ex\,\, c.\)
\(\int 3\,\,dx = \int 3x^{0}\,\,dx = \dfrac{3x^{0 + 1}}{(0 + 1)} \,\,dx = \dfrac{3x}{1} + C = 3x + C\)
\(when\)
\(x \neq -1\)
\(and\)
\(C = any\,\,real\,\,number\)
\(ex\,\, a.\)
\(\int 5x^{3}\,\,dx = \dfrac{5x^{3 + 1}}{(3 + 1)}\,\,dx = \dfrac{5x^{4}}{4} + C \)
\(ex\,\, b.\)
\(\int 10x^{4}\,\,dx = \dfrac{10x^{4 + 1}}{(4 + 1)}\,\,dx = \dfrac{10x^{5}}{5} + C = 2x^{5} + C\)
\(ex\,\, c.\)
\(\int 3\,\,dx = \int 3x^{0}\,\,dx = \dfrac{3x^{0 + 1}}{(0 + 1)} \,\,dx = \dfrac{3x}{1} + C = 3x + C\)