What is the integral of e^x-3cos(x) ?

The integral of e^x-3cos(x) is e^x-3sin(x)+C

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integral of e^x-3cos(x)

\int e^{x} - 3 cos (x) d x

e^{x} - 3 sin (x) + C

Solution steps

\int e^{x} - 3 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 3 cos (x) d x

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

\int 3 cos (x) d x = 3 sin (x)

= e^{x} - 3 sin (x)

Add a constant to the solution

= e^{x} - 3 sin (x) + C

\int sin^{3} (6 x) cos (6 x) d x

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

\int \frac{2 x ^{3} - x + 3}{( x ^{2} - 1 ) ^{2}} d x

\int \frac{4 t}{t ^{2} + 1} d t

\int x 3^{- x^{2}} d x

What is the integral of e^x-3cos(x) ?
The integral of e^x-3cos(x) is e^x-3sin(x)+C