Express the integrand as a sum of partial fractions and evaluate the integral.
-$$\int \frac { 60 } { t ^ { 3 } + 4 t ^ { 2 } - 5 t } d t$$
A) $- 12 \ln | t | + 10 \ln | t - 1 | + 2 \ln | t + 5 | + C$
B) $- 12 \ln | t | + 10 \ln \left| t ^ { 2 } - 1 \right| + C$
C) $- 2 \ln | t | + 10 \ln | t - 1 | - 2 \ln | t + 5 | + C$
D) $- \frac { 12 } { t } + 10 \ln | t - 1 | + 2 \ln | t + 5 | + C$

Question

Quizplus · Accepted Answer

The given integral can be solved by first factoring the denominator as $t(t^2 + 4t - 5)$, which further factors into $t(t-1)(t+5)$. Then, using partial fraction decomposition, the integrand can be expressed as a sum of fractions that can be integrated individually to yield the result in option A.

Express the Integrand as a Sum of Partial Fractions and Evaluate