Evaluate $\int \frac{x^{2}-x+5}{x} d x$ .
A) $\ln |x|\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}+5 x\right)+C$
B) $\frac{x^{2}}{2}-x+5 \ln |x|+C$
C) $\frac{2 x}{3}+\frac{10}{x}+C$
D) $\frac{x^{2}}{2}-x+\frac{10}{x^{2}}+C$

Question

Quizplus · Accepted Answer

The integral can be simplified by dividing each term in the numerator by $x$, resulting in $\int (x-1+5/x) dx$, which integrates to $\frac{x^2}{2} - x + 5\ln|x| + C$.

Evaluate ∫x2−x+5xdx\int \frac{x^{2}-x+5}{x} d x∫xx2−x+5​dx A) ln⁡∣x∣(x33−x22+5x)+C\ln |x|\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}+5 x\right)+Cln∣x∣(3x3​−2x2​+5x)+C B) x22−x+5ln⁡∣x∣+C\frac{x^{2}}{2}-x+5 \ln |x|+C2x2​−x+5ln∣x∣+C

Evaluate $\int \frac{x^{2}-x+5}{x} d x$
A) $\ln |x|\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}+5 x\right)+C$ B) $\frac{x^{2}}{2}-x+5 \ln |x|+C$