What is the integral of x^2-3/x+cos(x)-2/(sqrt(x)) ?

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

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integral of x^2-3/x+cos(x)-2/(sqrt(x))

\int x^{2} - \frac{3}{x} + cos (x) - \frac{2}{x} d x

\frac{x ^{3}}{3} - 3 ln ∣ x ∣ + sin (x) - 4 x + C

Solution steps

\int x^{2} - \frac{3}{x} + cos (x) - \frac{2}{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 x^{2} d x - \int \frac{3}{x} d x + \int cos (x) d x - \int \frac{2}{x} d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

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

= \frac{x ^{3}}{3} - 3 ln ∣ x ∣ + sin (x) - 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 3 ln ∣ x ∣ + sin (x) - 4 x + C

\int_{- 2}^{1} x^{- 4} d x

\int \frac{1}{( 1 + 5 x ) 5 x} d x

\frac{d}{d x} (\frac{3}{x ^{2}} - \frac{4}{x ^{3}})

\int_{0}^{1} \frac{ln ( x )}{5 x} d x

y = 2 (x + y) \frac{d y}{d x}

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