Use integration by parts to find the integral.
-$\int 7 x \ln x d x$
A) $\frac{x^{2}}{2} \ln x-\frac{x^{2}}{4}+C$
B) $\frac{7}{2} x^{2} \ln x-\frac{7}{4} x^{2}+C$
C) $\frac{7}{2} x \ln x-\frac{7}{4} x+C$
D) $\frac{7}{2} x^{2} \ln x-\frac{x^{2}}{4}+C$

Question

Quizplus · Accepted Answer

Using integration by parts, let $ u = \ln x $ and $ dv = 7x \, dx $. Then $ du = \frac{1}{x} \, dx $ and $ v = \frac{7}{2} x^2 $. The integral becomes $\frac{7}{2} x^2 \ln x - \int \frac{7}{2} x^2 \cdot \frac{1}{x} \, dx = \frac{7}{2} x^2 \ln x - \frac{7}{4} x^2 + C$.

Use Integration by Parts to Find the Integral ∫7xln⁡xdx\int 7 x \ln x d x∫7xlnxdx

Use Integration by Parts to Find the Integral $\int 7 x \ln x d x$