Question

evaluate the following indefinite integral.
int \frac { 1 } { 7 x ^ { 7 } } d x
int \frac { 1 } { 7 x ^ { 7 } } d x = square (type an exact answer.)

Explanation:

Step1: Rewrite the integrand

$$\int\frac{1}{7x^{7}}dx=\frac{1}{7}\int x^{-7}dx$$

Step2: Apply the power rule for integration

The power rule is $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n
eq - 1$). Here $n=-7$.
$$\frac{1}{7}\times\frac{x^{-7 + 1}}{-7+1}+C=\frac{1}{7}\times\frac{x^{-6}}{-6}+C$$

Step3: Simplify the expression

$$\frac{1}{7}\times\frac{x^{-6}}{-6}+C=-\frac{1}{42x^{6}}+C$$

Answer:

$-\frac{1}{42x^{6}}+C$