9 soal jawab integral ~ Orang Indonesia

1. ∫ √x dx = ∫ x^1/2dx

= 1/½+1 x^1/2+1+ c

= 2/3 x^3/2+ c

2. ∫ dx/√x dx = ∫ x ^-1/2dx

= 1/-½+1 x^-1/2+1 + c

= 2 x^1/2+ c

3. ∫ cos 5x dx = 1/5 sin 5x + c

4. ∫ cos³x sinx dx = -∫ z³dz missal z =cos x

= -1/4 z⁴ + c dz = - sinx dx

= -1/4 cos⁴x + c -dz = sinx dx

5. ∫ x. √x²-4 dx = ½ ∫√z dz missal z = x²-4

= ½. 1/½+1 z^1/2+1+c dz = 2x dx

= ½. 2/3 z^3/2 + c ½ dz= x dx

= 2/6. Z^3/2+ c

= 1/3 (x²-4)^3/2 +c

6. ∫ x. e^x2+5dx = ½ ∫e^z dz missal z = x²+5

= ½ e^z+c dz = 2x dx

= ½ e^x2+5+c 1/2dz= x dx

7. ∫ xdx/x²-3 = ½ ∫ dz/z missal z = x²-3

= ½ z ln z + c dz = 2x dx

= ½ ln(x²-3) ½ dz = x dx

8. ∫ x tan(x²-5) dx = ½ ∫ tan z dz missal1 z = x²-5 → ½ dz = x dx

= ½ ∫ sin z/ cos z dz missal2 y = cos z → -dy = sin z dz

= - ½ ∫ dy/y

= -½ ln y + c

= -½ ln cos z + c

= -½ ln cos(x²-5) + c

9. ∫ dx / x²+2x+2 = ∫ dx / x²-2x-1+1

= ∫ dx / (x+1)²+ 1 misal z = x+1

= ∫ dz / z²+1 dz = dx

= tan^-1 z + c

= tan^-1 x+1 +c

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