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

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

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integral of e^x+cos(x)

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

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

Solution steps

\int e^{x} + cos (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 e^{x} d x = e^{x}

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

= e^{x} + sin (x)

Add a constant to the solution

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

\int \frac{5 x + 3}{7 x - 1} d x

\frac{y}{5}

\frac{d ^{2}}{d x ^{2}} (12 x^{3} - 32 x^{2})

\frac{d}{d x} (x - \frac{2}{x})

x^{5}