Specify the substitution you would choose to evaluate the integrals. $$\int ( t + 4 ) e ^ { t ^ { 2 } + 8 t + 1 } d t$$
A) $u = t + 4$
B) $U = e ^ { t ^ { 2 } + 8 t + 1 }$
C) $u = t ^ { 2 } + 8 t + 1$
D) $u = ( t + 4 ) e$

Question

Quizplus · Accepted Answer

The derivative of $t^2 + 8t + 1$ is $2t + 8$, which closely matches the other factor in the integrand, $t + 4$, after considering a constant factor. This makes $u = t^2 + 8t + 1$ a suitable substitution for simplifying the integral.

Specify the Substitution You Would Choose to Evaluate the Integrals ∫(t+4)et2+8t+1dt\int ( t + 4 ) e ^ { t ^ { 2 } + 8 t + 1 } d t∫(t+4)et2+8t+1dt

Specify the Substitution You Would Choose to Evaluate the Integrals $\int ( t + 4 ) e ^ { t ^ { 2 } + 8 t + 1 } d t$