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)

Add a constant to the solution

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

y = \frac{2 x ^{2} + 2 x + 4}{x}

\int \frac{10}{x ^{3}} d x

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

\int_{0}^{1} 3 x 5^{x} d x

y^{^{''}} + 2 y^{^{'}} - 10 y = 0