Use integration by parts to find the integral below. $\int \ln x ^ { 3 } d x$
A) $\ln x ^ { 4 } - 3 x ^ { 4 } + C$
B) $x \ln x ^ { 4 } - 4 x ^ { 4 } + C$
C) $\ln x ^ { 4 } - x ^ { 4 } + C$
D) $x \ln x ^ { 3 } - 3 x + C$
E) $4 x \ln x ^ { 4 } - 4 x + C$

Question

Quizplus · Accepted Answer

Using integration by parts, let $ u = \ln x^3 $ and $ dv = dx $. Then $ du = \frac{3}{x} dx $ and $ v = x $. The integral becomes $ x \ln x^3 - \int 3 dx = x \ln x^3 - 3x + C $.

Use Integration by Parts to Find the Integral Below ∫ln⁡x3dx\int \ln x ^ { 3 } d x∫lnx3dx

Use Integration by Parts to Find the Integral Below $\int \ln x ^ { 3 } d x$