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Integral Calculus help?

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∫(z^3 -1) / (z+2 ) dz? How do you solve this one?

asked Nov 16, 2014 in CALCULUS by anonymous

1 Answer

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The Function is image.

The Degree of the Numerator is higher than the Degree of Denominator, So first we divide (z³ - 1) by (z+2) using long division method.

Consider (z³-1)/(z+2).

Divide the first term of the dividend by the first term of the divisor z3/z= z2

So, the first term of the quotient is z2. Multiply (z+2) by z2 and subtract.

image

Divide the first term of the dividend by the first term of the divisor -2z2/z= -2z

So, the first term of the quotient is -2z. Multiply (z+2) by -2z and subtract.

image

Divide the first term of the dividend by the first term of the divisor 4z/z= 4

So, the first term of the quotient is 4. Multiply (z+2) by 4 and subtract.

image

Therefore, Substitute image in the integral.

image

Therefore image.

answered Nov 17, 2014 by Lucy Mentor

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