Question

Evaluate integral (1/4+x^2) dx​

Answer 1

$\sf{\qquad\qquad\huge\underline{{\sf Answer}}}$

We know :

$\qquad \dashrightarrow \: \displaystyle \sf {\int }^{}x {}^{n} \: dx = \dfrac{{x}^{n + 1}}{n + 1} + c$

Now, Let's evaluate ~

$\qquad \dashrightarrow \: \displaystyle \sf {\int }^{} \bigg( \frac{1}{4} + {x}^{2} \bigg)dx$

$\qquad \dashrightarrow \: \displaystyle \sf {\int }^{} \bigg( \frac{1}{4} {x}^{0} + {x}^{2} \bigg)dx$

$\qquad \dashrightarrow \: \displaystyle \sf \frac{1}{4} \dfrac{x {}^{0 + 1} }{1} + \dfrac{{x}^{2 +1 } }{2 + 1} + c$

$\qquad \dashrightarrow \: \displaystyle \sf \frac{1}{4} {x {}^{} }{} + \dfrac{{x}^{3} }{3} + c$

[ note c is constant added, because the that is indefinite integral ]

That's the answer~ ask me if you have doubts