0-pi-x-sin-x-1-cos-2-x-dx-0-pi-1-1-cos-3-x-sin-3-x-dx-0-pi-2-x-cos-x-sin-x-tan-2-x-cot-2-x-dx-0-1-tan-1-1-x-2-dx-

Question Number 167416 by Coronavirus last updated on 16/Mar/22

∫_( 0) ^( π) ((x.sin (x))/(1+cos^2 (x) ))dx ∫_0 ^( π) (1/(1+cos^3 (x) +sin^3 (x) ))dx ∫_0 ^(π/2) ((x.cos(x)sin(x))/(tan^2 (x)+ cot^2 (x) ))dx ∫_0 ^( 1) tan^(−1) ((√(1−x^2 )))dx

$$\int_{\:\mathrm{0}} ^{\:\pi} \:\frac{{x}.\mathrm{sin}\:\left({x}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({x}\right)\:}{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\:\pi} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}^{\mathrm{3}} \left({x}\right)\:+\mathrm{sin}^{\mathrm{3}} \left({x}\right)\:}{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{x}.\mathrm{cos}\left(\mathrm{x}\right)\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)+\:\mathrm{cot}^{\mathrm{2}} \left(\mathrm{x}\right)\:}\mathrm{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx} \\ $$$$ \\ $$

Commented by Coronavirus last updated on 16/Mar/22