What is the integral of 4e^x+cos(x/5) ?

The integral of 4e^x+cos(x/5) is 4e^x+5sin(x/5)+C

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integral of 4e^x+cos(x/5)

\int 4 e^{x} + cos (\frac{x}{5}) d x

4 e^{x} + 5 sin (\frac{x}{5}) + C

Solution steps

\int 4 e^{x} + cos (\frac{x}{5}) 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 4 e^{x} d x + \int cos (\frac{x}{5}) d x

\int 4 e^{x} d x = 4 e^{x}

\int cos (\frac{x}{5}) d x = 5 sin (\frac{x}{5})

= 4 e^{x} + 5 sin (\frac{x}{5})

Add a constant to the solution

= 4 e^{x} + 5 sin (\frac{x}{5}) + C

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

\int \frac{tan ^{4} ( x )}{sec ^{7} ( x )} d x

\int 3 sin^{2} (t) cos (t) d t

\int x^{4} e^{3 x} d x

\frac{d}{d x} (2 sec (2 x) tan (2 x))

What is the integral of 4e^x+cos(x/5) ?
The integral of 4e^x+cos(x/5) is 4e^x+5sin(x/5)+C