Hitunglah integral tak tentu berikut.a. integral 2 dx b.

a. 2x + C, b. (3/4)x^4 + (2/3)x^3 - 2x^2 + x + C, c. (1/3)x^3 + (2/3)x^(3/2) + C

Pembahasan

Untuk menyelesaikan integral tak tentu berikut, kita akan menggunakan aturan dasar integral:

a. Integral 2 dx
Integral dari konstanta k terhadap x adalah kx + C.
Jadi, integral 2 dx = 2x + C.

b. Integral (3x^3 + 2x^2 - 4x + 1) dx
Kita gunakan aturan pangkat: integral x^n dx = (x^(n+1))/(n+1) + C.
Integral 3x^3 dx = (3x^(3+1))/(3+1) = (3x^4)/4
Integral 2x^2 dx = (2x^(2+1))/(2+1) = (2x^3)/3
Integral -4x dx = (-4x^(1+1))/(1+1) = (-4x^2)/2 = -2x^2
Integral 1 dx = x
Jadi, integral (3x^3 + 2x^2 - 4x + 1) dx = (3/4)x^4 + (2/3)x^3 - 2x^2 + x + C.

c. Integral (x^2 + akar(x)) dx
Kita ubah akar(x) menjadi x^(1/2).
Integral x^2 dx = (x^(2+1))/(2+1) = x^3/3
Integral x^(1/2) dx = (x^(1/2 + 1))/(1/2 + 1) = (x^(3/2))/(3/2) = (2/3)x^(3/2)
Jadi, integral (x^2 + akar(x)) dx = (1/3)x^3 + (2/3)x^(3/2) + C.

Jawaban:
a. 2x + C
b. (3/4)x^4 + (2/3)x^3 - 2x^2 + x + C
c. (1/3)x^3 + (2/3)x^(3/2) + C