What is the integral of e^x-5cos(x) ?

The integral of e^x-5cos(x) is e^x-5sin(x)+C

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integral of e^x-5cos(x)

\int e^{x} - 5 cos (x) d x

e^{x} - 5 sin (x) + C

Solution steps

\int e^{x} - 5 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 5 cos (x) d x

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

\int 5 cos (x) d x = 5 sin (x)

= e^{x} - 5 sin (x)

Add a constant to the solution

= e^{x} - 5 sin (x) + C

\int (3 x - 4) (x + 3) d x

\int \frac{e ^{x}}{1 + 3 e ^{- x}} d x

\int 1 - ∣ x ∣ d x

\int (x^{2} - cos (x)) d x

What is the integral of e^x-5cos(x) ?
The integral of e^x-5cos(x) is e^x-5sin(x)+C