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Question Number 185873 by test1234 last updated on 29/Jan/23

$$\left(1\right)\int \pi x^2+\sqrt{\frac{{xe}^{\pi }}{x^2}}dx=?$$$$\left(2\right)\int \frac{\ln \left(x\right)+\ln \left(\frac{-z}{x}\right)}{x^z}+z^{x}dx=?$$

Answered by JDamian last updated on 29/Jan/23

$$\left(2\right)\int \frac{\ln \left(\cancel{x}\frac{-z}{\cancel{x}}\right)}{x^z}+e^{x\cdot \ln z}dx=$$$$=\ln (-z)\int x^{-z}dx+\frac{e^{x\cdot \ln z}}{\ln z}$$

Answered by aba last updated on 29/Jan/23

$$\left(1\right)\int \pi {\mathrm{x}}^2+\sqrt{\frac{{\mathrm{xe}}^{\pi }}{{\mathrm{x}}^2}}\mathrm{dx}=\int (\pi {\mathrm{x}}^2+\sqrt{{\mathrm{e}}^{\pi }}.{\mathrm{x}}^{-\frac{1}{2}})\mathrm{dx}$$$$=\frac{1}{3}\pi {\mathrm{x}}^3+2\sqrt{{\mathrm{e}}^{\pi }\mathrm{x}}+\mathrm{k}$$

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