What is the integral of 3x^{-3}+sin(x) ?

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

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integral of 3x^{-3}+sin(x)

\int 3 x^{- 3} + sin (x) d x

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

Solution steps

\int 3 x^{- 3} + 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 3 x^{- 3} d x + \int sin (x) d x

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

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

= - \frac{3}{2 x ^{2}} - cos (x)

Add a constant to the solution

= - \frac{3}{2 x ^{2}} - cos (x) + C

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

\frac{\partial}{\partial θ} (r (θ) \cdot cos (θ))

e^{r t}

\int_{- π}^{π} sin^{3} (x) d x

x \to 0 + lim (x ln (tan (3 x)))

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