Solve ∫ (3^-1X4^-1)X5^-1j

$$\int ( 3 ^ { - 1 } X 4 ^ { - 1 } ) X 5 ^ { - 1 } j$$

Evaluate

$$\frac{jxX^{2}}{60}+С$$

Solution Steps

Multiply X and X to get X^{2}.

$$\int 3^{-1}X^{2}\times 4^{-1}\times 5^{-1}j\mathrm{d}x$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\int \frac{1}{3}X^{2}\times 4^{-1}\times 5^{-1}j\mathrm{d}x$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$\int \frac{1}{3}X^{2}\times \frac{1}{4}\times 5^{-1}j\mathrm{d}x$$

Multiply \frac{1}{3} and \frac{1}{4} to get \frac{1}{12}.

$$\int \frac{1}{12}X^{2}\times 5^{-1}j\mathrm{d}x$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\int \frac{1}{12}X^{2}\times \frac{1}{5}j\mathrm{d}x$$

Multiply \frac{1}{12} and \frac{1}{5} to get \frac{1}{60}.

$$\int \frac{1}{60}X^{2}j\mathrm{d}x$$

Find the integral of \frac{X^{2}j}{60} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{X^{2}j}{60}x$$

Simplify.

$$\frac{X^{2}jx}{60}$$

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.

$$\frac{X^{2}jx}{60}+С$$

Differentiate w.r.t. x

$$\frac{jX^{2}}{60}$$