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Question
Verify the following using the concept of integration as an antiderivative
`int (x^3"d"x)/(x + 1) = x - x^2/2 + x^3/3 - log|x + 1| + "C"`
Solution
`"d"/"dx"(x - x^2/2 + x^3/3 - log|x + 1| + "C")`
= `1 - (2x)/2 + (3x^2)/3 - 1/(x + 1)`
= `1 - x + x^2 - 1/(x + 1)`
= `x^3/(x + 1)`.
Thus `(x - x^2/2 + x^3/3 - log|x + 1| + "C") = intx^3/(x + 1) "d"x`
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