Монгол Бодлогын Сан

Заавар: Орлуулах аргаар бод: $$\int_a^b g[f(x)]\cdot f^\prime(x)\,\mathrm{d}x=\int_a^b g[f(x)]\,\mathrm{d}f(x)=\int_{f(a)}^{f(b)}g(t)\,\mathrm{d}t$$

Бодолт: $$\displaystyle\int_1^{e^2}\dfrac{\ln x}{x}\,\mathrm{d}x=\int_1^{e^2}\ln x\cdot(\ln x)^\prime\,\mathrm{d}x=\int_{\ln1}^{\ln e^2}t\,\mathrm{d}t=$$ $$=\int_0^2t\,\mathrm{d}t=\dfrac{t^2}{2}\bigg|_0^2=\dfrac{2^2}{2}-\dfrac{0^2}{2}=2$$