Question

For which of the following integrands will the table method for parts produce an antiderivative?


`e^xtan(x)`

`x^3sin(x)`

`e^xln(x)`
None of these.

Thank you so much in advance!

Answer 1

x³ sin(x)

Explanation:

Tabular method is a special form of integration by parts. It works by taking derivatives of u and integrals of dv. You multiply diagonally, then sum the results, alternating the signs.

The important thing to note is that this will produce an antiderivative only if the derivatives of u eventually become 0. So the correct choice is x³ sin(x), because the derivatives of x³ eventually becomes 0:

d/dx (x³) = 3x²

d/dx (3x²) = 6x

d/dx (6x) = 6

d/dx (6) = 0