Question

Integrate the following. ∫" align="absmiddle" class="latex-formula">
Option A: $x^{5}$
Option B: $5x^{5} +C$
Option C:$5x^{5}$
Option D: $x^{5} + C$

Answer 1

D is the best option in my opinion hope you get it correct

Answer 2

Answer:

$\displaystyle D) {x}^{5} + \rm C$

Step-by-step explanation:

we would like to integrate the following Integral:

$\displaystyle \int 5 {x}^{4} \, dx$

well, to get the constant we can consider the following Integration rule:

$\displaystyle \int c{x} ^{n} \, dx = c\int {x}^{n} \, dx$

therefore,

$\displaystyle 5\int {x}^{4} \, dx$

recall exponent integration rule:

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

so let,

• $n = 4$

Thus integrate:

$\displaystyle = 5\left( \frac{ {x}^{4+ 1} }{4 + 1} \right)$

simplify addition:

$\displaystyle = 5\left( \frac{ {x}^{5} }{5} \right)$

reduce fraction:

$\displaystyle = {x}^{5}$

finally we of course have to add the constant of integration:

$\displaystyle \boxed{ {x}^{5} + \rm C}$

hence,

our answer is D)