INTEGRALS — Maths STD 12 Science — Question

1. $\tan\text{x}-\cot\text{x+c}$

Solution:

$\int\sec^2\text{x}.\text{cosec}^2\text{xdx}$

$=\int\frac{{1}}{{\cos^2\text{x.}\sin^2\text{x}}}\text{dx}$

$=\int\frac{{{{\cos^2\text{x.}\sin^2\text{x}}}}}{{\cos^2\text{x.}\sin^2\text{x}}}\text{dx}$

$=\int\frac{{{{\cos^2\text{x.}}}}}{{\cos^2\text{x}\sin^2\text{x}}}+\frac{{{{\sin^2\text{x}}}}}{{\cos^2\text{x.}\sin^2\text{x}}}\text{dx}$

$=\int(\text{cosec}^2\text{x}+\sec^2\text{x})\text{dx}$

$=-\cot\text{x}+\tan\text{x}+\text{c}$

$=\tan\text{x}-\cot\text{x+c}$