[SOLVED] integrating

goldgophermn · February 8th 2007, 02:07 PM

How do you integrate

1) (1/30) e^(-x/30)

2) 1 - (25/x^2)

Thanks!!

**topsquark** · February 8th 2007, 02:41 PM

Originally Posted by goldgophermn

How do you integrate

1) (1/30) e^(-x/30)

2) 1 - (25/x^2)

Thanks!!

1)
$\int \frac{1}{30}e^{-x/30} dx$

Let y = -x/30, then dy = -dx/30.
$\int \frac{1}{30}e^{-x/30} dx = \frac{1}{30} \int e^y (-30dy)= -e^y + C = -e^{-x/30} + C$

2)
$\int \left ( 1 - \frac{25}{x^2} \right ) dx = \int \, dx - \frac{1}{25} \int \frac{dx}{x^2}$

$= x - \frac{1}{25} \cdot \frac{-1}{x} + C = x + \frac{1}{25x} + C$

-Dan

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