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

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

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integral of 2sin(x)-e^x

integral

2 sin (x) - e^{x}

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

Solution steps

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

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

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

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

Add a constant to the solution

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

sin (x + 2 y)

(1 + x)^{0.5}

f (t) = e^{t} \cdot t^{\frac{1}{2}}

(x + 4 x - 5 i)^{3}

\frac{e ^{x}}{( e ) ^{2}} x + 1

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