How do you evaluate the integral $int3e^(x)-5e^(2x) dx$ ?

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Answer 1 · 2014-09-25T20:12:47

$int 3e^x-5e^{2x}dx=3e^x-5/2e^{2x}+C$

Let us look at some details.

Remember:

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

$int e^{kx} dx=e^{kx}/k+C$

Now, let us work on the integral.

$int 3e^x-5e^{2x}dx$

by applying integral on each term,

$=int 3e^x dx -int 5e^{2x}dx$

by pulling constants out of the integrals

$=3int e^x dx-5int e^{2x}dx$

by applying the formulas above,

$=3e^x-5e^{2x}/2+C$

How do you evaluate the integral int3e^(x)-5e^(2x) dxint3e^(x)-5e^(2x) dx?