Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\displaystyle\int{ \frac{ 1 }{ 2 { x }^{ \frac{ 1 }{ 2 } } + { x }^{ \frac{ 3 }{ 2 } } } }d x$$

Answer

$$(d*x)/(2*sqrt(x)+x^(3/2))$$

Solution


Convert \({x}^{\frac{1}{2}}\) to square root.
\[\int 1 \, \frac{d}{2\sqrt{x}+{x}^{\frac{3}{2}}}dx\]
Use this rule: \(\int a \, dx=ax+C\).
\[\frac{dx}{2\sqrt{x}+{x}^{\frac{3}{2}}}\]
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