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CBSE Class 12 · 2020 · Indefinite IntegralsVery Short Answer

Find

\int x^{4} lo g x d x

Answer: $\frac{x ^{5} lo g x}{5} - \frac{x ^{5}}{25} + C$

Solution

By parts with

u = lo g x

(first by ILATE) and

d v = x^{4} d x

, so

d u = \frac{1}{x} d x

and

v = \frac{x ^{5}}{5}

:

\int x^{4} lo g x d x = lo g x \cdot \frac{x ^{5}}{5} - \int \frac{1}{x} \cdot \frac{x ^{5}}{5} d x = \frac{x ^{5} lo g x}{5} - \frac{1}{5} \int x^{4} d x .

= \frac{x ^{5} lo g x}{5} - \frac{x ^{5}}{25} + C .

\frac{x ^{5} lo g x}{5} - \frac{x ^{5}}{25} + C

CBSE Class 12 Board · 2020 · Subjective

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