Can someone confirm this U sub is legal?

[Saladsamurai]

$$\int e^{-4x} dx\\ = \int e^x *e^{-3x}$$ let u=e^x so du=e^x dx

so $$\int u^{-3} du$$

=$$-\frac{1}{2}e^{-2x}+c$$

Thanks,
Casey

 

[mattmns]

You made a mistake in the first line, however, it is easy to fix the resulting steps. It should be $e^x \times e^{-5x}$. I think your method works, however, I think the substitution $u = -4x$ is much easier.

Also, remember that you can check to see if your answer is correct by taking the derivative at the end.

 

[asd1249jf]

$$\int e^{-4x} dx\\ = \int e^{-x} *e^{-3x}$$

you forgot the negative sign on $$e^x$$.

But as mattmns above me suggested, just use u = -4x

 

[Saladsamurai]

You made a mistake in the first line, however, it is easy to fix the resulting steps. It should be $e^x \times e^{-5x}$. I think your method works, however, I think the substitution $u = -4x$ is much easier.

Also, remember that you can check to see if your answer is correct by taking the derivative at the end.

Oh yeah..it's not a power to a power.

I did it both ways, and yes they are equal,...and u=-4x is easier.

$$-\frac{1}{4}e^{-4x}$$

Thanks,
Casey