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Selesaikanlah integral ∫ 3 x ( x 2 3 − 1 ) d x

Selesaikanlah integral $\int 3 x (\frac{3}{x ^{2}} - 1) d x$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style equals integral open parentheses fraction numerator 9 x over denominator x squared end fraction minus 3 x close parentheses d x end style$

$equals integral size 14px 9 over size 14px x size 14px d size 14px x size 14px minus integral size 14px 3 size 14px x size 14px space size 14px d size 14px x equals 9 integral size 14px 1 over size 14px x size 14px d size 14px x size 14px minus size 14px 3 integral size 14px x size 14px space size 14px d size 14px x size 14px equals size 14px 9 size 14px ln begin mathsize 14px style open vertical bar x close vertical bar end style size 14px minus size 14px 3 begin mathsize 14px style left parenthesis fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent right parenthesis end style size 14px plus size 14px C equals size 14px 9 size 14px ln begin mathsize 14px style open vertical bar x close vertical bar end style size 14px minus size 14px 3 begin mathsize 14px style left parenthesis 1 half x squared right parenthesis end style size 14px plus size 14px C size 14px equals size 14px 9 size 14px ln begin mathsize 14px style open vertical bar x close vertical bar end style size 14px minus size 14px 3 over size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px C$