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