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

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

Evaluate : $\textstyle\int$ cos⁻¹(sin x) dx.

Evaluate : $\textstyle\int\!{\frac{\ d x}{\sin^{2}x\cos^{2}x}}$ .

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

Write the value of : $\textstyle\int{\frac{\sec^{2}x}{\operatorname{cosec}^{2}x}}d x.$

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$

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

Given $\textstyle\int e^{x}(\tan x+1)\sec x\,d x=e^{x}f(x)+c.$ Write f(x) satisfying the above.

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

Find : $\textstyle\int\!{\frac{1}{x(1+\log x)}}\,d x$

Find : $\int{\frac{3\,x}{3\,x-1}}\,d x$

Evaluate $\textstyle\int{\frac{2}{1+\cos2x}}\,d x$

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

Write the value of $\textstyle\int\!{\frac{2-3\sin x}{\cos^{2}x}}\,d x$.