Evaluate the integral.
-$$\int \left( x ^ { 2 } - 3 x \right) e ^ { x } d x$$
A) $\frac { 1 } { 3 } x ^ { 3 } e ^ { x } - \frac { 3 } { 2 } x ^ { 2 } e ^ { x } + C$
B) $e ^ { x } \left[ x ^ { 2 } - 3 x + 3 \right] + C$
C) $e ^ { x } \left[ x ^ { 2 } - 5 x + 5 \right] + C$
D) $e ^ { x } \left[ x ^ { 2 } - 5 x - 5 \right] + C$

Question

Quizplus · Accepted Answer

This integral can be solved using integration by parts or recognizing it as a product of a polynomial and an exponential function. The correct answer involves applying integration by parts multiple times or recognizing a pattern in the derivative of the product of $x^n e^x$. The result is $e^x [x^2 - 5x + 5] + C$, which matches option C.

Evaluate the Integral ∫(x2−3x)exdx\int \left( x ^ { 2 } - 3 x \right) e ^ { x } d x∫(x2−3x)exdx

Evaluate the Integral $\int \left( x ^ { 2 } - 3 x \right) e ^ { x } d x$