Integral Calculus help?

Question

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

Answer 1

The Function is .

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.

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.

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.

Therefore, Substitute in the integral.

Therefore .