Question

What is the integration of 1/root x dx​

Answer 1

Given :

The integration of (1/√x) dx

To find :

The value of the given integration.

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

To solve this mathematical problem, we have to know more about integration.

What is integration?

• Integration can be defined as the "opposite process of the differentiation".
• Like differentiation, integration problems can be solved by applying its own set of formulas and methods (eg. integration by parts, partial fraction etc.).

Here, we will be using the general formulas of integration to solve this problem.

So,

$= \int \frac{1}{ \sqrt{x} } \: dx$

$= \int \frac{1}{ {x}^{ \frac{1}{2} } } \: dx$

$= \int( {x})^{ - \frac{1}{2} } \: dx$

$= \frac{ {x}^{ (- \frac{1}{2} + 1) } }{ - \frac{1}{2} + 1 } + C$

$= \frac{ {x}^{ \frac{1}{2} } }{ \frac{1}{2} } + C$

$= \sqrt{x} \div \frac{1}{2} + C$

$= 2 \sqrt{x} + C$

(This will be the final result. Here, the 'C' is constant of integration.)

Used formula :

$\int {x}^{n} \: dx = \frac{ {x}^{n + 1} }{n + 1} + C$

Hence, the result will be (2√x + C)

Answer 2

Given: The integration of $(1/\sqrt{x} ) dx$

To find:

The value of the given integration.

Solution: We can simply solve this mathematical problem by using the following mathematical process.

To solve this mathematical problem, we have to know more about integration.

What is integration?

Integration can be defined as the "opposite process of the differentiation".

Like differentiation, integration problems can be solved by applying its own set of formulas and methods (eg. integration by parts, partial fraction etc.)

Here, we will be using the general formulas of integration to solve this problem.

So,

= $\int\limits {\frac{1}{\sqrt{x} } } \, dx$

= $\int\limits {\frac{1}{{x^1/2} } } \, dx$

= $\int\limits (x)^-\frac{1}{2} dx$

= $=\frac{x^{-1/2+1}}{-\frac{1}{2}+1 }+C$

$=\frac{x^{1/2}}{\frac{1}{2}}+C$

$=\sqrt{x} \div \frac{1}{2} +C$

$=2\sqrt{x} + C$

(This will be the final result. Here, the 'C' is the constant of integration.)

Used formula :

$\int\limits x^ndx=\frac{x^{n+1}}{n+1} +C$

Hence, the result will be $(2\sqrt{x} + C)$

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