Question

integerat x^4+x^2+1/2(x^2+1)​

Answer 1

Answer:

$I = \dfrac{x^{5} }{5} + \dfrac{x}{2} + C$

Step-by-step explanation:

Given-

$I = \int\ {x^{4}+\dfrac{(x^{2}+1) }{2(x^{2}+1) }  } \, dx$

$I = \int\ {x^{4}+\dfrac{1}{2} } \, dx$

$= \int\ {x^{4} } \, dx + \int\ {\dfrac{1}{2} } \, dx$

$= \int\ {x^{4} } \, dx + \dfrac{1}{2}\int {1} \, dx$

We know that-

$\int\ {x^{n} } \, dx = \dfrac{x^{n+1} }{n+1}$

$= \dfrac{x^{5} }{5} + \dfrac{1}{2}(x) + C$

$I = \dfrac{x^{5} }{5} + \dfrac{x}{2} + C$

Where C is an integral constant.