Question

Integral de (x+1)(3x-2)dx
Resposta tem q dar -2x+x³+1/2 x²+c

Answer 1

∫ (x+1)(3x-2) dx = ∫ 3x²+x-2 dx = ∫ 3x² dx + ∫ x dx - 2 ∫ dx
∫ 3x² dx = 3 ∫ x² dx = 3x³/3 = x³ + c
∫ x dx = x²/2 = 1/2 x² + c
2 ∫ dx = 2x + c

Logo, temos:
x³ + 1/2 x² - 2x + c

Answer 2

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$\displaystyle\sf{\int (x+1)\cdot(3x-2)~dx=\int (3x^2-2x+3x-2)~dx}\\\displaystyle\sf{\int (3x^2+x-2)~dx=\diagup\!\!\!3\cdot\dfrac{1}{\diagup\!\!\!3}x^3+\dfrac{1}{2}x^2-2x+k}\\\displaystyle\sf{\int (3x^2+x-2)~dx=x^3+\dfrac{1}{2}x^2-2x+k\checkmark}$