Evaluate using integration by parts.
-$\int(2 x-1) \ln (21 x) d x$
A) $\left(x^{2}-x\right) \ln (21 x)-x^{2}+x+C$
B) $\left(x^{2}-x\right) \ln (21 x)-\frac{x^{2}}{2}+2 x+C$
C) $\left(\frac{x^{2}}{2}-x\right) \ln (21 x)-\frac{x^{2}}{4}+x+C$
D) $\left(x^{2}-x\right) \ln (21 x)-\frac{x^{2}}{2}+x+C$

Question

Quizplus · Accepted Answer

Integration by parts formula is $\int u \, dv = uv - \int v \, du$. Let $u = \ln(21x)$ and $dv = (2x-1)dx$. Then $du = \frac{1}{x}dx$ and $v = x^2 - x$. Applying the formula gives the result in choice D.

Evaluate Using Integration by Parts ∫(2x−1)ln⁡(21x)dx\int(2 x-1) \ln (21 x) d x∫(2x−1)ln(21x)dx

Evaluate Using Integration by Parts $\int(2 x-1) \ln (21 x) d x$