# Evaluate the indefinite integral of int (9 + x^{1/4}) dx.

## Question:

Evaluate the indefinite integral of {eq}\int (9 + x^{1/4}) dx {/eq}.

## Rules Of Integration:

We have a table of integrals which includes formulas to solve the integrals of different functions. Two of them which are helpful in solving the current problem are:

\begin{align} &(i)\,\, \int x^n dx = \frac{x^{n+1}}{n+1}+C \\ &(ii) \,\, \int dx = x+C \end{align}

## Answer and Explanation:

Two of the formulas of integration which are helpful in solving the current problem are:

\begin{align} &(i)\,\, \int x^n dx = \dfrac{x^{n+1}}{n+1}+C \\ &(ii) \,\, \int dx = x+C \end{align}

The given integral is:

\begin{align} \int\left(9+x^{1 / 4}\right) d x & =9 \int dx + \int x^{1/4} dx \\ & = 9x + \dfrac{x^{5/4}}{(5/4)}+C & \text{(Using the above formulas)} \\ & = 9x + \dfrac{4}{5} x^{5/4}+C \end{align}

Therefore, {eq}\boxed{\mathbf{\int\left(9+x^{1 / 4}\right) d x =9x + \dfrac{4}{5} x^{5/4}+C }} {/eq}