Question

integration of
$\frac{3}{2 \sqrt{x} }$
​

Answer 1

Given , the function is $\tt{\frac{3}{2 \sqrt{x} }}$

Integrating wrt x , we get

$\implies \tt \int{\frac{3}{2 \sqrt{x} }} \: \: dx$

$\implies \tt \frac{3}{2} \int{{ \frac{1}{ \sqrt{x} } }} \: \: dx$

$\implies \tt \frac{3}{2} \int{{ {(x)}^{ \frac{ - 1}{2} } } } \: \: dx$

$\implies \tt \frac{3}{2} \{ \frac{2 {(x)}^{ \frac{1}{2} } }{1} \}$

$\implies \tt 3 {(x)}^{ \frac{1}{2} }$

Hence , the anti - derivative is $\tt 3 {(x)}^{ \frac{1}{2} }$

Remmember :

$\implies \tt \int{{ {(ax)} }} \: \: dx = a \int{(x)} \: \: dx$

$\implies \tt \int{{ {(x)}^{n} }} \: \: dx = \frac{ {(x)}^{n + 1} }{n + 1}$

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Answer 2

Given , the function is

$\tt{\frac{3}{2 \sqrt{x} }} </p><p>$

Integrating wrt x , we get

$\implies \tt \int{\frac{3}{2 \sqrt{x} }} \: \: dx \\ </p><p></p><p>\implies \tt \frac{3}{2} \int{{ \frac{1}{ \sqrt{x} } }} \: \: dx</p><p> \\ </p><p>\implies \tt \frac{3}{2} \int{{ {(x)}^{ \frac{ - 1}{2} } } } \: \: dx</p><p> \\ </p><p>\implies \tt \frac{3}{2} \{ \frac{2 {(x)}^{ \frac{1}{2} } }{1} \}</p><p></p><p>\implies \tt 3 {(x)}^{ \frac{1}{2} }</p><p>$

Hence , the anti - derivative is

$\tt 3 {(x)}^{ \frac{1}{2} }</p><p>$

Remmember :

$\implies \tt \int{{ {(ax)} }} \: \: dx = a \int{(x)} \: \: dx \\ </p><p></p><p>\implies \tt \int{{ {(x)}^{n} }} \: \: dx = \frac{ {(x)}^{n + 1} }{n + 1}$

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