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Hasil dari integral fraction numerator x plus 1 over denominator square root of x squared plus 2 x minus 2 end root end fraction straight d x equals... 

Pembahasan Soal:

Untuk mencari penyelesaian dari integral fraction numerator x plus 1 over denominator square root of x squared plus 2 x minus 2 end root end fraction straight d x dapat dilakukan dengan pemisalan.

Misal:
 

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared plus 2 x minus 2 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 2 x plus 2 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 2 open parentheses x plus 1 close parentheses end cell row cell integral open parentheses fraction numerator straight d u over denominator straight d x end fraction close parentheses space straight d x end cell equals cell integral 2 open parentheses x plus 1 close parentheses space straight d x end cell row cell integral straight d u end cell equals cell 2 integral open parentheses x plus 1 close parentheses space straight d x end cell row cell 1 half integral straight d u end cell equals cell integral open parentheses x plus 1 close parentheses space straight d x end cell end table

Oleh karena itu, didapat perhitungan berikut ini.

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

Jadi, hasil dari integral fraction numerator x plus 1 over denominator square root of x squared plus 2 x minus 2 end root end fraction straight d x equals square root of x squared plus 2 x minus 2 end root plus c.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Juli 2021

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