## Related questions with answers

Question

Find the general antiderivative of f and check your answer by differentiating.

$f ( x ) = 12 e ^ { x } - 5 x ^ { - 2 }$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3The antiderivative of the given function we can find as:

$\begin{align*} \int f(x) dx&=\int (12e^x-5x^{-2})dx\\ &= \int12 e^x dx - \int 5 x^{-2} dx&&\text{[Sum Rule]}\\ &= 12\int e^x dx - 5 \int x^{-2} dx&&\text{[Multiples Rule]}\\ &=12 e^x -5 \cdot \dfrac{x^{-2+1}}{-2+1} +C&&\text{[Power Rule]}\\ &=12 e^x +5 x^{-1}+ C \end{align*}$

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