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}


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Integration Problems in Calculus: Solutions & Examples

from AP Calculus AB & BC: Homework Help Resource

Chapter 13 / Lesson 13
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