Evaluate the integral $\int _ { 1 } ^ { 9 } \frac { 8 x ^ { 2 } - 3 x + 7 } { x } d x$
A) $616 + 7 \ln 9$
B) $296 + 7 \ln 9$
C) $616 + 9 \ln 7$
D) $296 + 9 \ln 7$

Question

Quizplus · Accepted Answer

The integral can be simplified by dividing each term in the numerator by $x$, resulting in $\int _ { 1 } ^ { 9 } (8x - 3 + \frac{7}{x}) dx$. Integrating term by term gives $4x^2 - 3x + 7\ln(x)$ evaluated from 1 to 9, which simplifies to $4(81) - 3(9) + 7\ln(9) - (4(1) - 3(1) + 7\ln(1))$, leading to $324 - 27 + 7\ln(9) - 4 + 3$, which simplifies to $296 + 7\ln(9)$.

Evaluate the Integral ∫198x2−3x+7xdx\int _ { 1 } ^ { 9 } \frac { 8 x ^ { 2 } - 3 x + 7 } { x } d x∫19​x8x2−3x+7​dx

Evaluate the Integral $\int _ { 1 } ^ { 9 } \frac { 8 x ^ { 2 } - 3 x + 7 } { x } d x$