Evaluate the following. ∫x31+x4 dx - Mathematics and Statistics

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Sum

Evaluate the following.

`int "x"^3/sqrt(1 + "x"^4)` dx

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Solution

Let I = `int "x"^3/sqrt(1 + "x"^4)` dx

Put 1 + x4 = t

∴ 4x3 . dx = dt

∴ x3 . dx = `1/4` dt

∴ I = `1/4 int "dt"/sqrt"t"`

`= 1/4 int "t"^((-1)/2)`dt

`= 1/4 * "t"^(1/2)/(1/2)` + c

`= 1/2 sqrt"t" + "c"`

∴ I = `1/2 sqrt(1 + "x"^4)` + c

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Chapter 5: Integration - EXERCISE 5.2 [Page 123]

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