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

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

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integral of 3e^x-sin(x)

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

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

Solution steps

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

\int 3 e^{x} d x = 3 e^{x}

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

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

Simplify

= 3 e^{x} + cos (x)

Add a constant to the solution

= 3 e^{x} + cos (x) + C

\int_{3}^{\infty} e^{- \frac{x}{5}} d x

\int (\frac{4}{1 - x ^{2}}) d x

\frac{2}{s ^{3} ( s ^{2} + 5 )}

\int_{0}^{1} t^{3} (4 + t^{4})^{3} d t

2 y^{^{''}} + 2 y + y = 0

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