What is the integral of e^x-8cos(x) ?

The integral of e^x-8cos(x) is e^x-8sin(x)+C

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integral of e^x-8cos(x)

\int e^{x} - 8 cos (x) d x

e^{x} - 8 sin (x) + C

Solution steps

\int e^{x} - 8 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 8 cos (x) d x

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

\int 8 cos (x) d x = 8 sin (x)

= e^{x} - 8 sin (x)

Add a constant to the solution

= e^{x} - 8 sin (x) + C

\int 5 x - 3 d x

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

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

\int \frac{cos ( 3 x )}{x ^{3}} d x

\int x^{- 2} x d x

What is the integral of e^x-8cos(x) ?
The integral of e^x-8cos(x) is e^x-8sin(x)+C