What is the integral of (2/x+3sin(x)-4ex) ?

The integral of (2/x+3sin(x)-4ex) is 2ln|x|-3cos(x)-2ex^2+C

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integral of (2/x+3sin(x)-4ex)

\int (\frac{2}{x} + 3 sin (x) - 4 e x) d x

2 ln ∣ x ∣ - 3 cos (x) - 2 e x^{2} + C

Solution steps

\int \frac{2}{x} + 3 sin (x) - 4 e 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 \frac{2}{x} d x + \int 3 sin (x) d x - \int 4 e x d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

\int 4 e x d x = 2 e x^{2}

= 2 ln ∣ x ∣ - 3 cos (x) - 2 e x^{2}

Add a constant to the solution

= 2 ln ∣ x ∣ - 3 cos (x) - 2 e x^{2} + C

\frac{d}{d x} (4 x - 8 y^{3})

y^{^{''}} + y^{^{'}} = x

\int_{0}^{1} (2 x + 1) e^{x^{2} + x} d x

\frac{\partial}{\partial x} (y^{2} arctan (x))

\frac{\partial}{\partial x} (\frac{x + y}{y - x})

What is the integral of (2/x+3sin(x)-4ex) ?
The integral of (2/x+3sin(x)-4ex) is 2ln|x|-3cos(x)-2ex^2+C