Pertanyaan

Tentukanintegral tak tentu berikut: h. ∫ ( x 3 + 6 x 5 ) + ( 3 x 2 + 6 ) d x

Tentukan integral tak tentu berikut:

h. $\int (x^{3} + 6 x^{5}) + (3 x^{2} + 6) d x$

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

integral tak tentu dari adalah .

integral tak tentu dari integral open parentheses x cubed plus 6 x to the power of 5 close parentheses plus open parentheses 3 x squared plus 6 close parentheses d x

integral open parentheses x cubed plus 6 x to the power of 5 close parentheses plus open parentheses 3 x squared plus 6 close parentheses d x

adalah

1 fourth x to the power of 4 plus x to the power of 6 plus x cubed plus 6 x plus straight C

Pembahasan

Rumus dasar integral yaitu: dengan sayarat , suatu konstanta Diperoleh penyelesaiannya yaitu: Dengan demikian, integral tak tentu dari adalah .

Rumus dasar integral yaitu:

$integral k x to the power of n space d x equals fraction numerator k over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus straight C$ dengan sayarat
, suatu konstanta

Diperoleh penyelesaiannya yaitu:

$integral open parentheses x cubed plus 6 x to the power of 5 close parentheses plus open parentheses 3 x squared plus 6 close parentheses d x equals integral x cubed space d x plus integral 6 x to the power of 5 space d x plus integral 3 x squared space d x plus integral 6 space d x equals fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus fraction numerator 6 over denominator 5 plus 1 end fraction x to the power of 5 plus 1 end exponent plus fraction numerator 3 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus 6 x plus straight C equals 1 fourth x to the power of 4 plus 6 over 6 x to the power of 6 plus 3 over 3 x cubed plus 6 x plus straight C equals 1 fourth x to the power of 4 plus x to the power of 6 plus x cubed plus 6 x plus straight C$

Dengan demikian, integral tak tentu dari integral open parentheses x cubed plus 6 x to the power of 5 close parentheses plus open parentheses 3 x squared plus 6 close parentheses d x adalah 1 fourth x to the power of 4 plus x to the power of 6 plus x cubed plus 6 x plus straight C .