$\int_{1}^{2} x^{3} \ln x d x=\ln 2-\frac{15}{4}$ .

Name: $\int_{1}^{2} x^{3} \ln x d x=\ln 2-\frac{15}{4}$ .
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Question

Quizplus · Accepted Answer

Using integration by parts, where $u = \ln x$ and $dv = x^3 dx$, we find the integral $\int_{1}^{2} x^{3} \ln x dx$ equals $\frac{7}{4} \ln 2 - \frac{7}{16}$, not $\ln 2 - \frac{15}{4}$.

∫12x3ln⁡xdx=ln⁡2−154\int_{1}^{2} x^{3} \ln x d x=\ln 2-\frac{15}{4}∫12​x3lnxdx=ln2−415​

$\int_{1}^{2} x^{3} \ln x d x=\ln 2-\frac{15}{4}$