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## anonymous one year ago integrate

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1. amistre64

what have you considered?

2. anonymous

|dw:1442184148009:dw|

3. amistre64

what is the derivative of: e^(kx) with respect to x? for some constant k

4. amistre64

ok, so this derivative looks similar to what we have, it differs by a sign right? lets alter its appearance some; multiply it by (-1/-1)

5. amistre64

$\int\frac{-1}{-1}\frac14e^{-x/4}dx$ $\int\frac{1}{-1}\frac{-1}4e^{-x/4}dx$ $\frac{1} {-1}\int\frac{-1}4e^{-x/4}dx$ or simply $-\int-\frac{1}4e^{-x/4}dx$

6. amistre64

we know an antiderivative of the integral so, we should certainly be able to use it for a solution

7. amistre64

u-subbing is a valid process, but i find that training yourself to see the possibilities of where it comes from is more conducive with timed tests :)

8. amistre64

|dw:1442184708371:dw|

9. amistre64

|dw:1442184778575:dw|

10. anonymous

Thank you so much @amistre64

11. amistre64

good luck

12. anonymous

put -x/4=t x=-4t dx=-4 dt $I=\frac{ 1 }{ 4 }\int\limits e^t(-4~dt)=-e^t+c=-e ^{\frac{ -x }{ 4 }}+c$

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