What is the integral of e^x-6sin(x) ?

The integral of e^x-6sin(x) is e^x+6cos(x)+C

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integral of e^x-6sin(x)

\int e^{x} - 6 sin (x) d x

e^{x} + 6 cos (x) + C

Solution steps

\int e^{x} - 6 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 6 sin (x) d x

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

\int 6 sin (x) d x = - 6 cos (x)

= e^{x} - (- 6 cos (x))

Simplify

= e^{x} + 6 cos (x)

Add a constant to the solution

= e^{x} + 6 cos (x) + C

\int y e^{6 y^{2}} d y

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

\int \frac{x ^{3} - 2 x ^{2} + 2 x - 5}{x ^{4} + 4 x ^{2} + 3} d x

\int \frac{1}{5 - x ^{2} - 6 x} d x

\int (1 + 5 x)^{- \frac{1}{2}} d x

What is the integral of e^x-6sin(x) ?
The integral of e^x-6sin(x) is e^x+6cos(x)+C