Solution: Assume $I=\int \sqrt{\tan x} \sec ^{4} x d x$ We can write the above equation as $\Rightarrow I=\int \sqrt{\tan x} \sec ^{2} x \sec ^{2} x d x$ Now, taking common $\begin{array}{l}...

Solution: Assume $I=\int \tan ^{5} x d x$ We can write the above equation as $\Rightarrow I=\int \tan ^{2} x \tan ^{3} x d x$ By using the standard formula $\Rightarrow I=\int\left(\sec ^{2}...

Solution: Assume $I=\int \sec ^{6} x \tan x d x$ We can write the above equation as $\Rightarrow I=\int \sec ^{5} x(\sec x \tan x) d x$ Substituting, $\sec x=t \Rightarrow \sec x \tan x d x=d t$, we...

Solution: Assume $I=\int \tan ^{5} x \sec ^{4} x d x$ We can write the above equation as $\Rightarrow I=\int \tan ^{5} x \sec ^{2} x \sec ^{2} x d x$ Taking $\tan ^{5} \mathrm{x}$ as common, we get...

Solution: Assume $I=\int \tan x \sec ^{4} x d x$ We can write the above equation as $\Rightarrow \mathrm{I}=\int \tan \mathrm{x} \sec ^{2} \mathrm{x} \sec ^{2} \mathrm{x} \mathrm{dx}$...

Solution: Assume $I=\int \tan ^{3} x \sec ^{2} x d x$ Assume $\tan \mathrm{x}=\mathrm{t}$, then $\Rightarrow \sec ^{2} x d x=d t$ On substituting the values of $x$, we get $\Rightarrow...