Final answer to the problem
The integral diverges.
Step-by-step Solution
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- Integrate by partial fractions
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- Product of Binomials with Common Term
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1
Factor the trinomial $x^2-2x-35$ finding two numbers that multiply to form $-35$ and added form $-2$
$\begin{matrix}\left(5\right)\left(-7\right)=-35\\ \left(5\right)+\left(-7\right)=-2\end{matrix}$
Learn how to solve definite integrals problems step by step online.
$\begin{matrix}\left(5\right)\left(-7\right)=-35\\ \left(5\right)+\left(-7\right)=-2\end{matrix}$
Learn how to solve definite integrals problems step by step online. Integrate the function (x+5)/(x^2-2x+-35) from 4 to 6. Factor the trinomial x^2-2x-35 finding two numbers that multiply to form -35 and added form -2. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Simplifying. Apply the formula: \int\frac{n}{x+b}dx=nsign\left(x\right)\ln\left(x+b\right)+C, where b=-7 and n=1.
Final answer to the problem
The integral diverges.
