Solve ∫ -3x^-05/-6x^05+18 wrt x=?

$$\int \frac { - 3 x ^ { - 05 } } { - 6 x ^ { 05 } + 18 } d x = ?$$

Evaluate

$$-\frac{x}{4}+С$$

Solution Steps

Multiply 0 and 5 to get 0.

$$\int \frac{-3x^{0}}{-6x^{0\times 5}+18}\mathrm{d}x$$

Calculate x to the power of 0 and get 1.

$$\int \frac{-3}{-6x^{0\times 5}+18}\mathrm{d}x$$

Multiply 0 and 5 to get 0.

$$\int \frac{-3}{-6x^{0}+18}\mathrm{d}x$$

Calculate x to the power of 0 and get 1.

$$\int \frac{-3}{-6+18}\mathrm{d}x$$

Add -6 and 18 to get 12.

$$\int \frac{-3}{12}\mathrm{d}x$$

Reduce the fraction \frac{-3}{12} to lowest terms by extracting and canceling out 3.

$$\int -\frac{1}{4}\mathrm{d}x$$

Find the integral of -\frac{1}{4} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$-\frac{x}{4}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-\frac{x}{4}+С$$

Differentiate w.r.t. x

$$-\frac{1}{4} = -0.25$$