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प्रश्न
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
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उत्तर
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/sqrtt`
`= 1/4 int t^((-1)/2)`dt
`= 1/4 * t^(1/2)/(1/2)` + c
`= 1/2 sqrtt + c`
∴ I = `1/2 sqrt(1 + x^4)` + c
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