evaluate the following indefinite integral. ∫1/(3x^6) dx ∫1/(3x^6) dx = □ (type an exact answer.)

Answer:

$-\frac{1}{15x^{5}}+C$

Explanation:

Step1: Rewrite the integrand

$\int\frac{1}{3x^{6}}dx=\frac{1}{3}\int x^{- 6}dx$

Step2: Apply power - rule for integration

The power - rule for integration is $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). Here $n=-6$, so $\frac{1}{3}\int x^{-6}dx=\frac{1}{3}\times\frac{x^{-6 + 1}}{-6+1}+C$

Step3: Simplify the expression

$\frac{1}{3}\times\frac{x^{-5}}{-5}+C=-\frac{1}{15x^{5}}+C$