Evaluate the integral. $\int \left( x ^ { 2 } + 1 \right) e ^ { 8 x + 2 } \mathrm {~d} x$
A) $\frac { e ^ { 8 x + 2 } } { 512 } \left( 64 x ^ { 2 } - 16 x - 66 \right) + C$
B) $\frac { e ^ { 8 x + 2 } } { 64 } \left( 64 x ^ { 2 } - 16 x + 66 \right) + C$
C) $\frac { e ^ { 8 x + 2 } } { 512 } \left( 64 x ^ { 2 } + 16 x - 66 \right) + C$
D) $\frac { e ^ { 8 x + 2 } } { 8 } \left( 64 x ^ { 2 } + 16 x - 66 \right) + C$
E) $\frac { e ^ { 8 x + 2 } } { 512 } \left( 64 x ^ { 2 } - 16 x + 66 \right) + C$

Question

Evaluate the integral.   $\int \left( x ^ { 2 } + 1 \right) e ^ { 8 x + 2 } \mathrm {~d} x$  
A) $\frac { e ^ { 8 x + 2 } } { 512 } \left( 64 x ^ { 2 } - 16 x - 66 \right) + C$
B) $\frac { e ^ { 8 x + 2 } } { 64 } \left( 64 x ^ { 2 } - 16 x + 66 \right) + C$
C) $\frac { e ^ { 8 x + 2 } } { 512 } \left( 64 x ^ { 2 } + 16 x - 66 \right) + C$
D) $\frac { e ^ { 8 x + 2 } } { 8 } \left( 64 x ^ { 2 } + 16 x - 66 \right) + C$
E) $\frac { e ^ { 8 x + 2 } } { 512 } \left( 64 x ^ { 2 } - 16 x + 66 \right) + C$

Quizplus · Accepted Answer

The integral can be solved using integration by parts. The correct choice matches the result obtained by applying integration by parts twice and simplifying the expression.

Evaluate the Integral ∫(x2+1)e8x+2 dx\int \left( x ^ { 2 } + 1 \right) e ^ { 8 x + 2 } \mathrm {~d} x∫(x2+1)e8x+2 dx

Evaluate the Integral $\int \left( x ^ { 2 } + 1 \right) e ^ { 8 x + 2 } \mathrm {~d} x$