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

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

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integral of (e^x-cos(x)+sin(x))

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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

\int 12 x - 4 d x

\int sec (t) (5 sec (t) + 4 tan (t)) d t

\int \frac{x ^{2}}{x ^{4} - 16} d x

\int sec (x) (3 sec (x) + 7 tan (x)) d x

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