What is the integral of e^x-2sin(x) ?

The integral of e^x-2sin(x) is e^x+2cos(x)+C

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integral of e^x-2sin(x)

\int e^{x} - 2 sin (x) d x

e^{x} + 2 cos (x) + C

Solution steps

\int e^{x} - 2 sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{x} d x - \int 2 sin (x) d x

\int e^{x} d x = e^{x}

\int 2 sin (x) d x = - 2 cos (x)

= e^{x} - (- 2 cos (x))

Simplify

= e^{x} + 2 cos (x)

Add a constant to the solution

= e^{x} + 2 cos (x) + C

\int \frac{( x ^{2} )}{3} d x

\int 5 x x^{2} + 9 d x

\int - x^{2} + 2 x + 3 d x

\int \frac{( x ^{3} + 4 x + 3 )}{x ^{4} + 5 x ^{2} + 4} d x

\int \frac{3 x - 4}{( x - 2 ) ( x + 1 )} d x

What is the integral of e^x-2sin(x) ?
The integral of e^x-2sin(x) is e^x+2cos(x)+C