Find the Integral 2/(x^2)

Problem

(∫_^)(2/(x2)*d(x))

Solution

1. Rewrite the integrand using a negative exponent to make it easier to apply the power rule for integration.

(∫_^)(2*x(−2)*d(x))

2. Apply the constant multiple rule by moving the constant coefficient outside the integral.

2*(∫_^)(x(−2)*d(x))

3. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C for n≠−1

2⋅(x(−2+1))/(−2+1)+C

4. Simplify the exponent and the denominator.

2⋅(x(−1))/(−1)+C

5. Simplify the expression by multiplying the constants and rewriting the negative exponent as a fraction.

−2*x(−1)+C

−2/x+C

Final Answer

(∫_^)(2/(x2)*d(x))=−2/x+C

Want more problems? Check here!