How do you integrate $\int x^{2} ln 5 x d x$ $int x^2 ln 5x dx$ using integration by parts?

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Answer 1 · 2016-02-17T00:41:29

Start by letting $u = ln (5 x)$ $u=ln(5x)$ and $dv=x^2\ dx$ to ultimately get $int \ x^2ln(5x)\ dx=1/3 x^3 ln(5x)-x^3/9+C$ .

If you let $u=ln(5x)$ and $dv=x^2\ dx$ , then $du=1/(5x) * 5\ dx=1/x\ dx$ and $v=x^3/3$ . Therefore

$\int\ x^2ln(5x)\ dx=uv-\int\ v\ du$

$=1/3 x^3 ln(5x)-\int\ x^2/3\ dx=1/3 x^3 ln(5x)-x^3/9+C$ .

How do you integrate int x^2 ln 5x dx ∫x2ln5xdxint x^2 ln 5x dx using integration by parts?