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

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

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integral of e^x+2cos(x)-3

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

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

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

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

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

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

\int 5^{4 x} d x

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