Solving: $\int_{-1}^{7}\frac{10y}{y^2-6y-16}dy$
Exercise
$\int_{-1}^7\left(\frac{10y}{y^2-6y-16}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function (10y)/(y^2-6y+-16) from -1 to 7. Rewrite the expression \frac{10y}{y^2-6y-16} inside the integral in factored form. Take out the constant 10 from the integral. Rewrite the fraction \frac{y}{\left(y+2\right)\left(y-8\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{5\left(y+2\right)}+\frac{4}{5\left(y-8\right)}\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Integrate the function (10y)/(y^2-6y+-16) from -1 to 7
Final answer to the exercise
The integral diverges.