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What is antiderivative of function y=e^(5x-14)?

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agneslund | Student, Undergraduate | eNoter

Posted August 15, 2011 at 1:24 AM via web

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What is antiderivative of function y=e^(5x-14)?

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giorgiana1976 | College Teacher | Valedictorian

Posted August 15, 2011 at 1:30 AM (Answer #1)

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The antiderivative of the given function is the primitive of the function, that differentiated with respect to x, gives the function y.

We'll have to take the inverse operation and to integrate the given function, to determine it's primitive.

`int` dy = `int` `e^(5x-14)` dx

We'll substitute 5x - 14 by t:

5x - 14 = t

We'll differentiste both sides:

5dx =dt => dx = dt/5

`int` `e^(5x-14)` dx = (1/5)`int` `e^(t)` dt = `e^(t)` /5 + C

Therefore, the requested antiderivative of the given function is Y = `e^(5x-14)` /5 + C.

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