Question

Find : $\textstyle\int{\frac{\sin^{6}x}{\cos^{8}x}}\,d x.$

Evaluate: $\textstyle\int(1-x){\sqrt{x}}\,d x~.$

Write the order of the differential equation: $\log\,\left(\frac{d^{2}y}{d x^{2}}\right)=\left(\frac{d y}{d x}\right)^{3}+x$

Find : $\textstyle\int{\frac{\sin^{2}\!x-\cos^{2}\!x}{\sin^{2}\!x\cos^{2}\!x}}\,d x$

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

Evaluate: $\textstyle\int\cot{x}(cosec x-1)e^{x}d x$ .

If ${\left[\begin{array}{l l}{x y}&{4}\\ {z+6}&{x+y}\end{array}\right]}\ ={\left[\begin{array}{l l}{8}&{w}\\ {0}&{6}\end{array}\right]},$ write the value of x + y + z.