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

x^{2} + 1, 1, 3

y^{^{'}} = 2 x

y^{^{''}} - 3 y^{^{'}} = 26 sin (2 t)

\int \frac{3 x ^{2}}{( 169 + x ^{2} ) ^{2}} d x

n = 1 \sum \infty \frac{4}{n + 1}