যোগজ নির্ণয় কর  :   $\int e^{x} \sec{x} \left ( 1 + \tan{x} \right ) dx$  

সমাধান: $\int e^{x} \sec x(1+\tan x) d x=\sec x \int e^{x} d x-\int\left\{\frac{d}{d x}(\sec x) \int e^{x} d x\right\} d x+\int e^{x} \sec x \tan x d x$ $=\mathrm{e}^{\mathrm{x}} \sec \mathrm{x}-\int \sec \mathrm{tan} x \cdot \mathrm{e}^{\mathrm{x}} \mathrm{dx}+\int \mathrm{e}^{\mathrm{x}} \sec \mathrm{tan} \mathrm{xdx}+\mathrm{c}_{1}=\mathrm{e}^{\mathrm{x}} \sec \mathrm{x}+\mathrm{c}$ (Ans.)

$\text { Or, } \left.\int e^{x}(\sec x+\sec x \tan x) d x=e^{x} \sec x+c ;\left[\int e^{x}\{f(x)\} f^{\prime}(x)\right\} d x=e^{x} f(x)+c\right]$