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Tentukan hasil dari begin mathsize 14px style integral fraction numerator 6 x squared space d x over denominator square root of x cubed minus 4 end root end fraction end style.

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Pembahasan Video:

Pembahasan Soal:

Untuk menyelesaikan integral dengan substitusi aljabar, soal harus diubah ke dalam bentuk begin mathsize 14px style integral u to the power of n space d u end style dengan begin mathsize 14px style u equals f left parenthesis x right parenthesis end style dan begin mathsize 14px style n not equal to 1 end style.

Diketahui integral dengan fungsi begin mathsize 14px style integral fraction numerator 6 x squared space d x over denominator square root of x cubed minus 4 end root end fraction end style.

Misal: begin mathsize 14px style u equals x cubed minus 4 end style maka begin mathsize 14px style d u equals 3 x squared space d x end style.

Penyelesaian integral tersebut adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 6 x squared space d x over denominator square root of x cubed minus 4 end root end fraction end cell equals cell integral fraction numerator left parenthesis 2 right parenthesis left parenthesis 3 x squared right parenthesis space straight d x over denominator left parenthesis x cubed minus 4 right parenthesis to the power of 1 half end exponent end fraction end cell row blank equals cell 2 integral left parenthesis x cubed minus 4 right parenthesis to the power of negative 1 half end exponent left parenthesis 3 x squared space straight d x right parenthesis space end cell row blank equals cell 2 integral u to the power of negative 1 half end exponent d u end cell row blank equals cell 2 open parentheses fraction numerator 1 over denominator negative begin display style 1 half end style plus 1 end fraction close parentheses times u to the power of negative 1 half plus 1 end exponent plus C end cell row blank equals cell 4 u to the power of 1 half end exponent plus C end cell row blank equals cell 4 times left parenthesis x cubed minus 4 right parenthesis to the power of 1 half end exponent plus C space end cell row blank equals cell 4 square root of x cubed minus 4 end root plus C end cell end table end style 

Jadi, hasil dari begin mathsize 14px style integral fraction numerator 6 x squared space d x over denominator square root of x cubed minus 4 end root end fraction end style adalah begin mathsize 14px style 4 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x cubed minus 4 end root end cell end table plus C end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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