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Pertanyaan

Tentukan integral-integral tak tentu berikut ini.

c) begin mathsize 14px style integral open parentheses 15 x to the power of 4 plus 18 x squared plus 6 x close parentheses straight d x end style  

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style integral open parentheses 15 x to the power of 4 plus 18 x squared plus 6 x close parentheses straight d x end style adalah begin mathsize 14px style 3 x squared left parenthesis x cubed plus 2 x plus 1 right parenthesis plus C end style. 

Pembahasan

Integral tak tentu merupakan sebuah bentuk operasi pengintegralan pada suatu fungsi menghasilkan suatu fungsi baru.

Nilai dari begin mathsize 14px style integral open parentheses 15 x to the power of 4 plus 18 x squared plus 6 x close parentheses straight d x end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses 15 x to the power of 4 plus 18 x squared plus 6 x close parentheses straight d x end cell row blank equals cell integral 15 x to the power of 4 space straight d x plus integral 18 x squared space straight d x plus integral 6 x space straight d x end cell row blank equals cell 15 integral x to the power of 4 space straight d x plus 18 integral x squared space straight d x plus 6 integral x space straight d x end cell row blank equals cell 15 open parentheses 1 fifth x to the power of 4 plus 1 end exponent plus C close parentheses plus 18 open parentheses 1 third x to the power of 2 plus 1 end exponent plus C close parentheses plus 6 open parentheses 1 half x to the power of 1 plus 1 end exponent plus C close parentheses end cell row blank equals cell 3 x to the power of 5 plus 6 x cubed plus 3 x squared plus C end cell row blank equals cell 3 x squared left parenthesis x cubed plus 2 x plus 1 right parenthesis plus C end cell end table end style              

Jadi, nilai dari begin mathsize 14px style integral open parentheses 15 x to the power of 4 plus 18 x squared plus 6 x close parentheses straight d x end style adalah begin mathsize 14px style 3 x squared left parenthesis x cubed plus 2 x plus 1 right parenthesis plus C end style. 

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