$\int {13^x} \, dx$ is

Consider the following statements $(A)$ and $(B)$:
$(A) \int_a^b \frac{d}{d x}(f(x)) d x = \frac{d}{d x} \int_a^b f(x) d x$
$(B) \frac{d}{d x} \left( \int f(x) d x \right) = f(x) + C$
Which one of the following is true?

$\int {\frac{{1 + x + \sqrt {x + {x^2}} }}{{\sqrt x + \sqrt {1 + x} }}\,dx} = $

Find the following integral: $\int \frac{2-3 \sin x}{\cos ^{2} x} d x$

$A$ gardener is digging a plot of land. As he gets tired,he works more slowly. After $t$ minutes,he is digging at a rate of $\frac{2}{\sqrt{t}}$ square metres per minute. How long will it take him to dig an area of $40$ square metres?

Find the integral of the function $\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$.