Evaluate the integral: int x^3 log x , dx | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Using integration by parts: $\int u \, dv = uv - \int v \, du$.Let $u = \log x$ and $dv = x^3 \, dx$.Then $du = \frac{1}{x} \, dx$ and $v = \frac{

Vedclass · Accepted Answer

$\frac{x^4}{16} [4 \log x - 1] + c$

Vedclass · Answer

(A) Using integration by parts: $\int u \, dv = uv - \int v \, du$.Let $u = \log x$ and $dv = x^3 \, dx$.Then $du = \frac{1}{x} \, dx$ and $v = \frac{x^4}{4}$.$\int x^3 \log x \, dx = (\log x) \left( \frac{x^4}{4} \right) - \int \left( \frac{x^4}{4} \right) \left( \frac{1}{x} \right) \, dx$.$= \frac{x^4}{4} \log x - \frac{1}{4} \int x^3 \, dx$.$= \frac{x^4}{4} \log x - \frac{1}{4} \left( \frac{x^4}{4} \right) + c$.$= \frac{x^4}{4} \log x - \frac{x^4}{16} + c$.$= \frac{x^4}{16} [4 \log x - 1] + c$.

Evaluate the integral: $\int x^3 \log x \, dx$

Similar Questions

$\int \frac{\cot^{-1}(e^x)}{e^x} dx$ is equal to:

If $f(x) = \lim _{n \rightarrow \infty} n^2 \left(x^{\frac{1}{n}} - x^{\frac{1}{n+1}}\right), x > 0$,then $\int x f(x) d x =$

The integral $\int {\cos \left( {{{\log }_e}x} \right)dx} $ is equal to: (where $C$ is a constant of integration)

$\int x{{\sin }^{ - 1}}x\;dx = $

Integrate the function: $x \log x$

Vedclass Test Series

Exam Paper Generator

Online Exam Module