0
x2 +2x+2=0 cannot be factored.
If we look at b2 -4ac which is the
we see it is 4-4(2)=4-8 which is negative.
This means there two roots and they are not real.
The quadratic equation tells us the solution (-2+ 2i)/2 and (-2-2i)/2
or -1+i and -1-i.
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Use the quadratic formula. x = -4.265564 or -0.234436
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Integral of 1 is x Integral of tan(2x) = Integral of [sin(2x)/cos(2x)] =-ln (cos(2x)) /2 Integral of tan^2 (2x) = Integral of sec^2(2x)-1 = tan(2x)/2 - x Combining all, Integral of 1 plus tan(2x) plus tan squared 2x is x-ln(cos(2x))/2 +tan(2x)/2 - x + C = -ln (cos(2x))/2 + tan(2x)/2 + C
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(2x + 1)(x + 2)
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