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Teacherbot 21 Oct, 09:02:19

  1. Integral de (cos(x) + tg(3x))dx: ∫(cos(x) + tan(3x))dx = ∫cos(x)dx + ∫tan(3x)dx = sin(x) - (1/3)ln|cos(3x)| + C

  2. Integral de ((x)/(sqrt(4+(4x^2)))dx: ∫(x/√(4+4x^2))dx = (1/2)∫(2x/√(4+4x^2))dx = (1/2)ln|√(4+4x^2) + 2x| + C

  3. Integral de (-sen(x) + 6 + sqrt(9-x))dx: ∫(-sin(x) + 6 + √(9-x))dx = -cos(x) + 6x + (2/3)(9-x)^(3/2) + C

  4. Integral de (((3x)/(x^2 -4))+(2/x^2 +1))dx: ∫((3x)/(x^2 -4) + (2/x^2 +1))dx = ∫(3x/(x-2)(x+2) + 2/(x^2 +1))dx = (3/2)ln|x-2| - (3/2)ln|x+2| + 2arctan(x) + C

  5. Integral de (2x^3 + 5x^2 - 3x + 4)dx: ∫(2x^3 + 5x^2 - 3x + 4)dx = (1/2)x^4 + (5/3)x^3 - (3/2)x^2 + 4x + C

  6. Integral de (e^x + 1/x + ln(x))dx: ∫(e^x + 1/x + ln(x))dx = e^x + ln|x| + xln(x) + C

  7. Integral de (sin(2x) + cos(3x))dx: ∫(sin(2x) + cos(3x))dx = -(1/2)cos(2x) + (1/3)sin(3x) + C

  8. Integral de (1/(x^2 + 4x + 5))dx: ∫(1/(x^2 + 4x + 5))dx = (1/2)ln|x^2 + 4x + 5| + C

  9. Integral de (x^2e^x + 2x)dx: ∫(x^2e^x + 2x)dx = x^2e^x + 2x^2/2 - 2∫xe^xdx = x^2e^x + x^2 - 2xe^x + 2e^x + C

  10. Integral de (3cos(x) - 2sin(x))dx: ∫(3cos(x) - 2sin(x))dx = 3sin(x) + 2cos(x) + C