What is the integral of 3cos(x)-1/(sqrt(x^3)) ?

The integral of 3cos(x)-1/(sqrt(x^3)) is 3sin(x)+2/(sqrt(x))+C

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integral of 3cos(x)-1/(sqrt(x^3))

\int 3 cos (x) - \frac{1}{x ^{3}} d x

3 sin (x) + \frac{2}{x} + C

Solution steps

\int 3 cos (x) - \frac{1}{x ^{3}} 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 \frac{1}{x ^{3}} d x

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

\int \frac{1}{x ^{3}} d x = - \frac{2}{x}

= 3 sin (x) - (- \frac{2}{x})

Simplify

= 3 sin (x) + \frac{2}{x}

Add a constant to the solution

= 3 sin (x) + \frac{2}{x} + C

\frac{d}{d x} (m (x - s) e^{k (x - d)} + p (x, d))

x \to \infty lim (3 x^{2} + 2)

\frac{d}{d x} (3 (e^{x} cos (x) - e^{x} sin (x)))

x \to 2 + lim (\frac{∣ x - 2 ∣}{x})

x \frac{d y}{d x} + 2 y = 3

What is the integral of 3cos(x)-1/(sqrt(x^3)) ?
The integral of 3cos(x)-1/(sqrt(x^3)) is 3sin(x)+2/(sqrt(x))+C