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Hasil dari ∫ 3 6 x 2 + 21 x − 4 4 x + 7 d x adalah ....

Hasil dari $\int \frac{4 x + 7}{3 6 x ^{2} + 21 x - 4} d x$ adalah ....

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Klaim

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

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Misalkan , sehingga Dengan metode integral subtitusi. Jadi, hasil dari adalah .

Misalkan u equals 6 x squared plus 21 x minus 4 , sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 6 x squared plus 21 x minus 4 end cell row cell d u end cell equals cell 12 x plus 21 space d x end cell row cell d u end cell equals cell 3 open parentheses 4 x plus 7 close parentheses space d x end cell row cell fraction numerator d u over denominator 3 end fraction end cell equals cell 4 x plus 7 space d x end cell end table$

Dengan metode integral subtitusi.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral fraction numerator 4 x plus 7 over denominator cube root of 6 x squared plus 21 x minus 4 end root end fraction d x end cell row blank equals cell integral fraction numerator 1 over denominator cube root of 6 x squared plus 21 x minus 4 end root end fraction times 4 x plus 7 space d x end cell row blank equals cell integral fraction numerator 1 over denominator cube root of u end fraction times fraction numerator d u over denominator 3 end fraction end cell row blank equals cell integral fraction numerator 1 over denominator 3 times cube root of u end fraction space d u end cell row blank equals cell 1 third integral fraction numerator 1 over denominator cube root of u end fraction space d u end cell row blank equals cell 1 third integral u to the power of negative 1 third end exponent space d u end cell row blank equals cell 1 third open square brackets fraction numerator 1 over denominator negative begin display style 1 third end style plus 1 end fraction u to the power of negative 1 third plus 1 end exponent plus C close square brackets end cell row blank equals cell 1 third open square brackets fraction numerator 1 over denominator negative begin display style 1 third end style plus begin display style 3 over 3 end style end fraction u to the power of negative 1 third plus 3 over 3 end exponent plus C close square brackets end cell row blank equals cell 1 third open square brackets fraction numerator 1 over denominator begin display style 2 over 3 end style end fraction u to the power of 2 over 3 end exponent plus C close square brackets end cell row blank equals cell 1 third open square brackets fraction numerator 3 over denominator begin display style 2 end style end fraction u to the power of 2 over 3 end exponent plus C close square brackets end cell row blank equals cell 1 half u to the power of 2 over 3 end exponent plus C end cell row blank equals cell 1 half open parentheses 6 x squared plus 21 x minus 4 close parentheses to the power of 2 over 3 end exponent plus C end cell end table$

Jadi, hasil dari $integral fraction numerator 4 x plus 7 over denominator cube root of 6 x squared plus 21 x minus 4 end root end fraction d x$ adalah

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