Question

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Answer 1

Step-by-step explanation:

$\sf Question\:3 \\ \\ \sf \int \frac {dx}{3{x}^{2} + 6x + 21 } \\ \\ \sf = \int \frac {dx} { 3 ( {x}^{2} + 2x + 7 )} \\ \\ \sf =\frac {1}{3} \int \frac {dx}{{x}^{2} + 2x + 1 + 6 } \\ \\ \sf= \frac {1}{3} \int \frac {1}{ {x +1 }^{2} + { \sqrt {6}}^{2}} \\ \\ \sf using\:standard\:formula\: \\ \\ \sf \boxed { \bold { \red { \int \frac {dx}{ {x}^{2} + {a}^{2}} = \frac {1}{a} {tan}^{-1} \frac {x}{a} }}} \\ \\ \sf so\:answer\:is = \frac {1}{\sqrt{6}} {tan}^{-1} \frac { x + 1 }{\sqrt{6}}\\ \\ \\ \\ \sf Question\:4 \\ \\ \sf The \: question \:is\: incomplete$

Answer 2

Answer:

Hope it helps you.......