Pertanyaan

∫ 6 x ( x 2 + 5 ) 3 d x = …

$\int 6 x (x^{2} + 5)^{3} d x = \dots$

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilai dari adalah

nilai dari integral 6 x open parentheses x squared plus 5 close parentheses cubed space straight d x

adalah 3 over 4 open parentheses x squared plus 5 close parentheses plus C

Pembahasan

Jadi, nilai dari adalah

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral 6 x open parentheses x squared plus 5 close parentheses cubed space straight d x end cell row cell Misal space u end cell equals cell x squared plus 5 end cell row cell maka space straight d u space end cell equals cell space 2 x space straight d x end cell row cell straight d x end cell equals cell fraction numerator straight d u over denominator 2 x end fraction end cell row cell integral 6 x open parentheses x squared plus 5 close parentheses cubed space straight d x end cell equals cell integral stack up diagonal strike 6 x end strike with 3 on top times u cubed space fraction numerator straight d u over denominator up diagonal strike 2 x end strike end fraction end cell row blank equals cell 3 integral u to the power of 3 space end exponent straight d u end cell row blank equals cell 3 times 1 fourth u to the power of 4 plus C end cell row blank equals cell 3 over 4 open parentheses x squared plus 5 close parentheses plus C end cell end table$

Jadi, nilai dari integral 6 x open parentheses x squared plus 5 close parentheses cubed space straight d x adalah 3 over 4 open parentheses x squared plus 5 close parentheses plus C