erikut! (Hint:Masih integral sederhana) i. f(x)=x^2-x f(x)=(3)/(x^2)-(2)/(x^3) j. f(x)=3x^2-pi x f(x)=(sqrt (2x))/(x)+(3)/(x^5) k. f(x)=27x^7+3x^5-45x^3 0. f(x)=(4x^6+3x^4)/(x^3) 1. f(x)=x^2(x^3+5x^2-3x +sqrt (3)) p. f(x)=(x^6-x)/(x^3)

Question

Pertanyaan

erikut! (Hint:Masih integral sederhana) i. f(x)=x^2-x f(x)=(3)/(x^2)-(2)/(x^3) j. f(x)=3x^2-pi x f(x)=(sqrt (2x))/(x)+(3)/(x^5) k. f(x)=27x^7+3x^5-45x^3 0. f(x)=(4x^6+3x^4)/(x^3) 1. f(x)=x^2(x^3+5x^2-3x +sqrt (3)) p. f(x)=(x^6-x)/(x^3)

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Answer 1

Berikut integral tak tentu dari fungsi-fungsi yang diberikan. Ingatlah bahwa konstanta integrasi (+C) selalu ditambahkan setelah integral tak tentu dihitung.

i.

* $f(x) = x^2 - x$
$\int f(x) dx = \int (x^2 - x) dx = \frac{x^3}{3} - \frac{x^2}{2} + C$

* $f(x) = \frac{3}{x^2} - \frac{2}{x^3} = 3x^{-2} - 2x^{-3}$
$\int f(x) dx = \int (3x^{-2} - 2x^{-3}) dx = \frac{3x^{-1}}{-1} - \frac{2x^{-2}}{-2} + C = -\frac{3}{x} + \frac{1}{x^2} + C$

j.

* $f(x) = 3x^2 - \pi x$
$\int f(x) dx = \int (3x^2 - \pi x) dx = x^3 - \frac{\pi x^2}{2} + C$

* $f(x) = \frac{\sqrt{2x}}{x} + \frac{3}{x^5} = \sqrt{2}x^{-1/2} + 3x^{-5}$
$\int f(x) dx = \int (\sqrt{2}x^{-1/2} + 3x^{-5}) dx = \sqrt{2}\frac{x^{1/2}}{1/2} + \frac{3x^{-4}}{-4} + C = 2\sqrt{2x} - \frac{3}{4x^4} + C$

k.

* $f(x) = 27x^7 + 3x^5 - 45x^3$
$\int f(x) dx = \int (27x^7 + 3x^5 - 45x^3) dx = \frac{27x^8}{8} + \frac{3x^6}{6} - \frac{45x^4}{4} + C = \frac{27x^8}{8} + \frac{x^6}{2} - \frac{45x^4}{4} + C$

o.

* $f(x) = \frac{4x^6 + 3x^4}{x^3} = 4x^3 + 3x$
$\int f(x) dx = \int (4x^3 + 3x) dx = x^4 + \frac{3x^2}{2} + C$

l.

* $f(x) = x^2(x^3 + 5x^2 - 3x + \sqrt{3}) = x^5 + 5x^4 - 3x^3 + \sqrt{3}x^2$
$\int f(x) dx = \int (x^5 + 5x^4 - 3x^3 + \sqrt{3}x^2) dx = \frac{x^6}{6} + x^5 - \frac{3x^4}{4} + \frac{\sqrt{3}x^3}{3} + C$

p.

* $f(x) = \frac{x^6 - x}{x^3} = x^3 - x^{-2}$
$\int f(x) dx = \int (x^3 - x^{-2}) dx = \frac{x^4}{4} + \frac{1}{x} + C$

Semoga penjelasan ini membantu! Ingatlah untuk selalu memeriksa jawaban Anda dan pastikan untuk memahami konsep dasar integral tak tentu.

Pertanyaan

erikut! (Hint:Masih integral sederhana) i. f(x)=x^2-x f(x)=(3)/(x^2)-(2)/(x^3) j. f(x)=3x^2-pi x f(x)=(sqrt (2x))/(x)+(3)/(x^5) k. f(x)=27x^7+3x^5-45x^3 0. f(x)=(4x^6+3x^4)/(x^3) 1. f(x)=x^2(x^3+5x^2-3x +sqrt (3)) p. f(x)=(x^6-x)/(x^3)

Jawaban

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