$\int {{e^x}\sin x(\sin x + 2\cos x)} \,dx = $

$\int e^{\tan x}(\sec ^{2} x+\sec ^{3} x \sin x) d x$ is equal to

$\int e^{x} \left[ \frac{\sin x + \cos x}{\cos^2 x} \right] dx$ is equal to:

$\int {{e^x}(1 - \cot x + {{\cot }^2}x)\,dx} $ equals

$\int \left[ \frac{\log x - 1}{1 + (\log x)^2} \right]^2 dx = $

Assertion $(A)$: $\int_2^e \left(\frac{1}{\log_e x} - \frac{1}{(\log_e x)^2}\right) dx = e - 2 \log_2 e$
Reason $(R)$: $\int_a^b e^x (f(x) + f'(x)) dx = e^b f(b) - e^a f(a)$