Question

find the following indefinite integral.

$$\int 6 x ^ { 5 } d x$$

$$\int 6 x ^ { 5 } d x = \square$$

Explanation:

Step1: Apply the constant multiple rule

The constant multiple rule states that $\int kf(x)dx = k\int f(x)dx$. So, $\int 6x^{5}dx = 6\int x^{5}dx$.

Step2: Use the power rule for integration

The power rule is $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n
eq - 1$). For $n = 5$, we have $\int x^{5}dx=\frac{x^{5+1}}{5 + 1}+C=\frac{x^{6}}{6}+C$.

Step3: Multiply by the constant

Substitute back into the expression from Step1: $6\times\frac{x^{6}}{6}+C$. The $6$ in the numerator and denominator cancels out.

Answer:

$x^{6}+C$