Evaluate the Integral integral of 1/(3x^2) with respect to x

Problem

(∫_^)(1/(3*x2)*d(x))

Solution

1. Rewrite the integrand by moving the constant factor outside the integral and expressing the power of x using a negative exponent.

(∫_^)(1/(3*x2)*d(x))=1/3*(∫_^)(x(−2)*d(x))

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

1/3*(∫_^)(x(−2)*d(x))=1/3*((x(−2+1))/(−2+1))+C

3. Simplify the expression by performing the arithmetic in the exponent and the denominator.

1/3*((x(−1))/(−1))+C=−1/3*x(−1)+C

4. Convert the negative exponent back into a fraction to reach the final form.

−1/3*x(−1)+C=−1/(3*x)+C

Final Answer

(∫_^)(1/(3*x2)*d(x))=−1/(3*x)+C

Want more problems? Check here!