$Evaluate {\int }_0^2\frac{3x}{x^2+1}dx$

$Find \int 4x{e}^{x^{2+1}}dx$

$Given that {\int }_0^{4}kx+2dx=12, and k is a cons\tan t, find the value of k.$

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$$\begin{gathered} What is the value of {\int }_3^{5}4x^{3}dx \\ \left(A\right) 192 \\ \left(B\right) 408 \\ \left(C\right) 544 \\ \left(D\right) 706 \end{gathered}$$

$$\begin{gathered} What is the derivative of {\left(e^{3x}+1\right)}^{-2}? \\ \left(A\right) -2e^{3x}{\left(e^{3x}+1\right)}^{-3} \\ \left(B\right) -2e^{3x}{\left(e^{3x}+1\right)}^{-1} \\ \left(C\right) -6e^{3x}{\left(e^{3x}+1\right)}^{-3} \\ \left(D\right) -6e^{3x}{\left(e^{3x}+1\right)}^{-1} \end{gathered}$$

$$\begin{gathered} The roots of the quadratic equation 2x^2+4x+5=0 and \alpha and \beta . \\ \left(i\right) Find the vlue of \alpha +\beta \\ \left(ii\right) Show that \frac{{\alpha }^2+{\beta }^2}{\alpha \beta }=-\frac{2}{5} \\ \left(iii\right) The roots of x^2+mx+p=0 are \frac{\alpha }{\beta }+2 and \frac{\beta }{\alpha }+2 \\ It is also given that \frac{{\alpha }^2+{\beta }^2}{\alpha \beta }=-\frac{2}{5} \\ Find the values of m and p where m and p are cons\tan t. \end{gathered}$$

$Evaluate {\int }_0^{\mathrm{\pi }}\sin 2x dx$

$Evaluate {\int }_0^1\frac{5}{\sqrt{e^x}} dx$

$$\begin{gathered} The region bounded by the curve y=\ln x,the axes and the line y=\ln 2, is rotated \\ about the y-axis. \\ Find the volum of the solid formed. \end{gathered}$$