Find the Integral (y^5-2y)/(y^3)

Problem

(∫_^)((y5−2*y)/(y3)*d(y))

Solution

1. Simplify the integrand by dividing each term in the numerator by the denominator y3

(y5)/(y3)−(2*y)/(y3)

2. Reduce the powers of y using the laws of exponents.

y2−2*y(−2)

3. Apply the sum rule for integration to integrate each term separately.

(∫_^)(y2*d(y))−(∫_^)(2*y(−2)*d(y))

4. Use the power rule for integration, (∫_^)(yn*d(y))=(y(n+1))/(n+1) for both terms.

(y3)/3−2*((y(−1))/(−1))+C

5. Simplify the signs and the expression.

(y3)/3+2/y+C

Final Answer

(∫_^)((y5−2*y)/(y3)*d(y))=(y3)/3+2/y+C

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