Solve ∫ logx^2pi

$$\int \log x ^ { 2 } \pi$$

Evaluate

$$\log(e)x\left(\ln(x^{2})+\ln(\pi )-2\right)+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{\int \ln(x^{2}\pi )\mathrm{d}x}{\ln(10)}$$

Simplify.

$$\frac{x\left(\ln(x^{2})+\ln(\pi )-2\right)}{\ln(10)}$$

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.

$$\frac{x\left(\ln(x^{2})+\ln(\pi )-2\right)}{\ln(10)}+С$$

Differentiate w.r.t. x

$$\log(e)\left(\ln(x^{2})+\ln(\pi )\right)$$