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Evaluate ∫ ∞ 0 E X 3 √ X D X - Applied Mathematics 2

Evaluate `int_0^inftye^(x^3)/sqrtx dx`

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Solution 1

`int_0^inftye^(x^3)/sqrtx dx` 

Put `x^3=t` 

∴` x=t^(1/3)` 

`dx=1/3 t ^(-2/3)`

∴ `I= int_0^infty e^-t.t^(1/6). 1/23.t^(-2/3) dt` 

∴ `I= int_0^infty e ^-t. t^  -5/6 dt`

∴` I= 1/3|bar1/6`

Solution 2

`int_0^inftye^(x^3)/sqrtx dx` 

Put `x^3=t` 

∴` x=t^(1/3)` 

`dx=1/3 t ^(-2/3)`

∴ `I= int_0^infty e^-t.t^(1/6). 1/23.t^(-2/3) dt` 

∴ `I= int_0^infty e ^-t. t^  -5/6 dt`

∴` I= 1/3|bar1/6`

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
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