Pertanyaan

Tentukan integral-integral tak tentu berikut ini. f) ∫ x ( x + 2 ) ⋅ ( x − 1 ) d x

Tentukan integral-integral tak tentu berikut ini.

f) $\int x (x + 2) \cdot (x - 1) d x$

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Jawaban terverifikasi

Jawaban

= .

Pembahasan

Ingat: . Jadi, = .

Ingat: $integral a x to the power of n space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C$ .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral x open parentheses x plus 2 close parentheses open parentheses x minus 1 close parentheses straight d x end cell row blank equals cell integral open parentheses x squared plus 2 x close parentheses open parentheses x minus 1 close parentheses straight d x end cell row blank equals cell integral open parentheses x cubed minus x squared plus 2 x squared minus 2 x close parentheses straight d x end cell row blank equals cell integral open parentheses x cubed plus x squared minus 2 x close parentheses straight d x end cell row blank equals cell fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 2 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus C end cell row blank equals cell 1 fourth x to the power of 4 plus 1 third x cubed minus x squared plus C end cell end table$

Jadi, = .