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

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

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integral of e^x-sin(x)

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

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

Solution steps

\int e^{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 sin (x) d x

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

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

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

Simplify

= e^{x} + cos (x)

Add a constant to the solution

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

e^{0.42 x}

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

x \to - 2 lim (\frac{2 x ^{2}}{x + 2})

\int 3 z d z

\int \frac{7}{x - 3} d x