What is the integral of 2sin(2x)-3e^x ?

The integral of 2sin(2x)-3e^x is -cos(2x)-3e^x+C

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integral of 2sin(2x)-3e^x

\int 2 sin (2 x) - 3 e^{x} d x

- cos (2 x) - 3 e^{x} + C

Solution steps

\int 2 sin (2 x) - 3 e^{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 2 sin (2 x) d x - \int 3 e^{x} d x

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

\int 3 e^{x} d x = 3 e^{x}

= - cos (2 x) - 3 e^{x}

Add a constant to the solution

= - cos (2 x) - 3 e^{x} + C

\int \frac{x ^{2} + 3}{x x ^{2} - 4} d x

\int x^{3} + x - \frac{1}{x ^{2}} d x

\int \frac{sin ( x )}{sin ( x )} d x

\int \frac{sin ^{3} ( x )}{1 + cos ^{2} ( x )} d x

\int \frac{( x + 1 )}{x ^{2} + x + 1} d x

What is the integral of 2sin(2x)-3e^x ?
The integral of 2sin(2x)-3e^x is -cos(2x)-3e^x+C