What is the integral of (3cos(x)-e^x+5/x) ?

The integral of (3cos(x)-e^x+5/x) is 3sin(x)-e^x+5ln|x|+C

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integral of (3cos(x)-e^x+5/x)

\int (3 cos (x) - e^{x} + \frac{5}{x}) d x

3 sin (x) - e^{x} + 5 ln ∣ x ∣ + C

Solution steps

\int 3 cos (x) - e^{x} + \frac{5}{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 cos (x) d x - \int e^{x} d x + \int \frac{5}{x} d x

\int 3 cos (x) d x = 3 sin (x)

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= 3 sin (x) - e^{x} + 5 ln ∣ x ∣

Add a constant to the solution

= 3 sin (x) - e^{x} + 5 ln ∣ x ∣ + C

\frac{d y}{d x} = 0. 4^{\frac{x}{3}}

3 y^{^{''}} + 5 y^{^{'}} = 0

\frac{\partial}{\partial y} (x y^{8} + x^{2} + y^{4})

\int \frac{sin ( 9 ln ( t ) )}{t} d t

n = 1 \sum \infty arctan (6 n)

What is the integral of (3cos(x)-e^x+5/x) ?
The integral of (3cos(x)-e^x+5/x) is 3sin(x)-e^x+5ln|x|+C