What is the integral of (4x-2/x+5sin(x)) ?

The integral of (4x-2/x+5sin(x)) is 2x^2-2ln|x|-5cos(x)+C

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integral of (4x-2/x+5sin(x))

\int (4 x - \frac{2}{x} + 5 sin (x)) d x

2 x^{2} - 2 ln ∣ x ∣ - 5 cos (x) + C

Solution steps

\int 4 x - \frac{2}{x} + 5 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 4 x d x - \int \frac{2}{x} d x + \int 5 sin (x) d x

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 5 sin (x) d x = - 5 cos (x)

= 2 x^{2} - 2 ln ∣ x ∣ - 5 cos (x)

Add a constant to the solution

= 2 x^{2} - 2 ln ∣ x ∣ - 5 cos (x) + C

x \to \infty lim ((4)^{x})

f^{^{'}} (x) = sec (2 x) tan (2 x) - \frac{4}{x ^{2}}

40 ln (2 x + 1)

n = 0 \sum \infty x^{n} \frac{1}{n}

\frac{d}{d x} (2 x^{3} + \frac{45 x ^{2}}{2} + 21 x + 4)

What is the integral of (4x-2/x+5sin(x)) ?
The integral of (4x-2/x+5sin(x)) is 2x^2-2ln|x|-5cos(x)+C