Integrate the function (x^2+6x+5)/(x^2+2x+1) from 0 to 0

 Exercise

$\int_0^0\left(\frac{x^2+6x+5}{x^2+2x+1}\right)dx$

 

Rewrite the expression $\frac{x^2+6x+5}{x^2+2x+1}$ inside the integral in factored form

$\int_{0}^{0}\frac{x^2+6x+5}{\left(x+1\right)^{2}}dx$

 

Factor the trinomial $x^2+6x+5$ finding two numbers that multiply to form $5$ and added form $6$

$\begin{matrix}\left(1\right)\left(5\right)=5\\ \left(1\right)+\left(5\right)=6\end{matrix}$

 

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

$\int_{0}^{0}\frac{\left(x+1\right)\left(x+5\right)}{\left(x+1\right)^{2}}dx$

 

Simplifying

$\int_{0}^{0}\frac{x+5}{x+1}dx$

 

When the bounds of an integral are the same, the integral is going to be equal to zero because the is no area to integrate

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.