$$\int\limits_{\sqrt{2}}^{\sqrt{3}} \frac{1}{\sqrt{4-x^2}} \,dx$$

$$\int\limits_{-3}^{4} (|x+2|-|x-1|)\,dx$$

$$\int\limits_0^1 x\cdot arctgx\,dx$$

$$\int\limits_3^4 \frac{x^2+3}{x-2} \,dx$$

$$\int\limits_0^{\pi/2} \sqrt{3\sin x+1}\cos x\,dx$$

$$\int\limits_1^e \ln^2 x\,dx$$

$$\int\limits_{\sqrt{2}}^{x} \frac{1}{t\sqrt{t^2-1}}\,dx=\frac{\pi}{12}$$

$$F(x)=\int\limits_0^1 t|t-x| \,dx$$

$$\int\limits_{-1}^{1} \frac{x^7-3x^5+7x^3-x}{\cos^2 x}\,dx=0$$

$$\int\limits_{0}^{\pi} xf(\sin x)\,dx = \frac{\pi}{2}\int\limits_{0}^{\pi} f(\sin x)\,dx$$