Evaluate - x3ln x d x

Here u = ln x ⇒ du=1/xdx and v=x^3⇒ dv=3x^2 dx I = 1/4x^4 ln x 1/4x^4 ln x 1/6x^4+c ...

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Byju's Answer

Standard VII

Mathematics

(a-b)^2 Expansion and Visualisation

Evaluate ∫ x3...

Question

Evaluate $\int x^{3} l n x d x$

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Solution

Here $u = l n x \Rightarrow d u = \frac{1}{x} d x$
and $v = x^{3} \Rightarrow d v = 3 x^{2} d x I = \frac{1}{4} x^{4} l n x - \frac{1}{4} x^{4} l n x - \frac{1}{6} x^{4} + c$

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Evaluate ∫x3 ln x dx

Here u=ln x⇒du=1xdx and v=x3⇒dv=3x2 dxI=14x4 ln x−14x4 ln x−16x4+c

Evaluate $\int x^{3} l n x d x$

Here $u = l n x \Rightarrow d u = \frac{1}{x} d x$
and $v = x^{3} \Rightarrow d v = 3 x^{2} d x I = \frac{1}{4} x^{4} l n x - \frac{1}{4} x^{4} l n x - \frac{1}{6} x^{4} + c$