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 = \frac{{x}^(n + 1)}{n + 1} + c`

Now, Let's evaluate ~

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

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

`\qquad \dashrightarrow \: \displaystyle \sf (1)/(4) \frac{x {}^(0 + 1) }{1} + \frac{{x}^(2 +1 ) }{2 + 1} + c`

`\qquad \dashrightarrow \: \displaystyle \sf (1)/(4) {x {}^{} }{} + \frac{{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