Pertanyaan

∫ ( ( 5 x − 2 ) 3 1 ) d x = ...

$\int (\frac{1}{( 5 x - 2 ) ^{3}}) d x = ...$ $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

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Error converting from MathML to accessible text.

Pembahasan

Ingat! Misalkan, , maka turunan pertama fungsi : Sehingga, . Maka, integral dari fungsi di atas: Jadi, .

Ingat!

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

Misalkan, u equals 5 x minus 2 , maka turunan pertama fungsi :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 1 times 5 x to the power of 1 minus 1 end exponent minus 0 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals 5 end table$

Sehingga, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight d u over denominator 5 end fraction end cell end table$ .

Maka, integral dari fungsi di atas:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript blank open parentheses 1 over open parentheses 5 x minus 2 close parentheses cubed close parentheses space d x end cell equals cell integral subscript blank open parentheses 1 over u cubed close parentheses space fraction numerator d u over denominator 5 end fraction end cell row blank equals cell integral subscript blank u to the power of negative 3 end exponent space fraction numerator d u over denominator 5 end fraction end cell row blank equals cell 1 fifth times fraction numerator 1 over denominator negative 3 plus 1 end fraction u to the power of negative 3 plus 1 end exponent plus C end cell row blank equals cell negative 1 over 10 u to the power of negative 2 end exponent plus C end cell row blank equals cell negative fraction numerator 1 over denominator 10 u squared end fraction plus C end cell row blank equals cell negative fraction numerator 1 over denominator 10 open parentheses 5 x minus 2 close parentheses squared end fraction plus C end cell end table$

Jadi, Error converting from MathML to accessible text. .