Question

$\int x^{\frac{1}{4}} dx = \square + c$

Explanation:

Step1: Recall the power rule for integration

The power rule for integration states that $\int x^n dx = \frac{x^{n + 1}}{n + 1} + C$, where $n
eq -1$.
Here, $n = \frac{1}{4}$.

Step2: Apply the power rule

Substitute $n = \frac{1}{4}$ into the power rule formula:

$$\begin{align*} \int x^{\frac{1}{4}} dx&=\frac{x^{\frac{1}{4}+ 1}}{\frac{1}{4}+ 1}+C\\ &=\frac{x^{\frac{5}{4}}}{\frac{5}{4}}+C\\ &=\frac{4}{5}x^{\frac{5}{4}}+C \end{align*}$$

Answer:

$\frac{4}{5}x^{\frac{5}{4}}$