Integrals of Exponential Functions

Key Questions

  • What is the antiderivative of n^x?

    By rewriting a bit,

    int n^x dx=int e^{(lnn)x}dx=e^{(lnn)x}/{lnn}+C=n^x/{lnn}+C

    I hope that this was helpful.

    Wataru · 3 · Oct 16 2014
  • How do you evaluate the integral inte^(-x) dx?

    The answer is I=-e^(-x)+C.

    This integral can be solved by a substitution:

    u=-x
    du=-dx
    -du=dx

    So, now we can substitute:

    int e^(-x)dx = int e^u (-du)
    =-int e^u du
    =-e^u + C

    and substitute back:
    =-e^(-x) + C

    For simple looking integrands, you should try a quick check to see if substitution works before trying harder integration methods.

    Amory W. · · Aug 20 2014
  • How do you evaluate the integral int3^(x) dx?

    Answer:

    int3^xdx=1/ln3 3^x+"c"

    Explanation:

    We want to find int3^xdx.

    Make the natural substitution u=3^x so du=3^xln3dx.

    So

    int3^xdx=1/ln3int1du=1/ln3 u+"c"=1/ln3 3^x+"c"

    Monzur R. · 1 · Mar 14 2018
  • What is the antiderivative of e^x?

    Since

    (e^x)'=e^x,

    we have

    int e^x dx=e^x+C.

    I hope that this was helpful.

    Wataru · 4 · Oct 16 2014

Questions

Introduction to Integration