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∫ 6 x 2 x 3 − 5 ​ d x = ....

 

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K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

 integral 6 x squared square root of x cubed minus 5 end root d x equals 4 over 3 open parentheses x cubed minus 5 close parentheses square root of x cubed minus 5 end root plus C 

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Pembahasan

Menggunakan metode subtitusi, akan dicari nilai integral di atas. Misalkan . Maka didapat Dengan demikian diperoleh Jadi,

Menggunakan metode subtitusi, akan dicari nilai integral di atas. Misalkan u equals x cubed minus 5. Maka didapat

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x cubed minus 5 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell fraction numerator d open parentheses x cubed minus 5 close parentheses over denominator d x end fraction end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 3 x squared end cell row cell d u end cell equals cell 3 x squared d x end cell row cell 2 cross times d u end cell equals cell 2 cross times 3 x squared d x end cell row cell 2 d u end cell equals cell 6 x squared d x end cell end table

Dengan demikian diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 6 x squared square root of x cubed minus 5 end root d x end cell equals cell integral open parentheses square root of x cubed minus 5 end root close parentheses 6 x squared d x end cell row blank equals cell integral square root of u 2 d u end cell row blank equals cell 2 integral square root of u d u end cell row blank equals cell 2 integral u to the power of 1 half end exponent d u end cell row blank equals cell 2 cross times fraction numerator 1 over denominator begin display style 1 half end style plus 1 end fraction u to the power of 1 half plus 1 end exponent plus C end cell row blank equals cell fraction numerator 2 over denominator begin display style 3 over 2 end style end fraction u to the power of 3 over 2 end exponent plus C end cell row blank equals cell 4 over 3 u square root of u plus C end cell row blank equals cell 4 over 3 open parentheses x cubed minus 5 close parentheses square root of x cubed minus 5 end root plus C end cell end table

Jadi, integral 6 x squared square root of x cubed minus 5 end root d x equals 4 over 3 open parentheses x cubed minus 5 close parentheses square root of x cubed minus 5 end root plus C 

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