Question

Evaluate $\textstyle\int\!{\frac{e^{2\,x}\,-\,e^{-2\,x}}{e^{2\,x}\,+\,e^{-2\,x}}}\,d x\,.$

If $\left(\begin{array}{l l }2x & 3\end{array}\right)$ $\left(\begin{array}{l l }1 & 2 \\ -3 & 0\end{array}\right)$ $\left(\begin{array}{l }x \\ 3\end{array}\right)$ = 0,

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.

Find the differential equation of the family of lines passing through the origin.

If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)

Write the value of $\textstyle\int\!{\frac{\ d x}{x^{2}+16}}$

Find $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$,If $\stackrel{\rightarrow}{a}$ = $-\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} -\stackrel{\wedge}{k}$.