Evaluate integral (1/4+x^2) dx

Question

asked Jun 17, 2023 2.1k views

1 Answer

Michael Malov · Answer 1 · 2023-06-21T14:14:29+0000

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

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