Find the integral of the function $\sin ^{-1}(\cos x)$.

If $\int \frac{x^2+1}{x^4+1} dx = f(x) + c$,then $f(x)$ is equal to

$\int \frac{5(x^6+1)}{x^2+1} \, dx =$ (Where $C$ is a constant of integration.)

If $\int \frac{x + 1}{x^2 + 1} dx = \tan^{-1} x + g(x) + c$, where $c$ is the constant of integration, then the function $g(x)$ is monotonically increasing in the interval

$A$ 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?

Evaluate the integral: $\int a^{3x + 3} dx$.