$\int \frac{t+5}{t^{2}+10 t+75} d t=\ln \left|t^{2}+10 t+75\right|+C$ .

Question

Quizplus · Accepted Answer

The integral $\int \frac{t+5}{t^{2}+10 t+75} d t$ does not directly simplify to $\ln \left|t^{2}+10 t+75\right|+C$. The correct approach involves completing the square in the denominator and possibly using a substitution to simplify the integral, which may lead to a different form involving logarithmic or arctan functions, depending on the specific substitution and simplification used.

∫t+5t2+10t+75dt=ln⁡∣t2+10t+75∣+C\int \frac{t+5}{t^{2}+10 t+75} d t=\ln \left|t^{2}+10 t+75\right|+C∫t2+10t+75t+5​dt=ln​t2+10t+75​+C

$\int \frac{t+5}{t^{2}+10 t+75} d t=\ln \left|t^{2}+10 t+75\right|+C$