Use integration by parts to find the given integral. (14x - 39)e^(-x) dx

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the formula of integration by parts, such that:

`int udv = uv - int vdu`

You need to consider `u = 14x - 39` and `dv = e^(-x)dx` such that:

`u = 14x - 39 => du = 14dx`

`dv = e^(-x)dx => v = -e^(-x) `

`int (14x - 39)e^(-x)dx = -(14x - 39)e^(-x) + 14int e^(-x)dx`

`int (14x - 39)e^(-x)dx = -(14x - 39)e^(-x) - 14e^(-x) + c`

Factoring out `-e^(-x)` yields:

`int (14x - 39)e^(-x)dx = -e^(-x)(14x - 39 + 14) + c`

Hence, evaluating the integral, using integration by parts, yields `int (14x - 39)e^(-x)dx = -e^(-x)(14x - 39 + 14) + c` .

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