Evaluate the Integral integral of 1/(7x^3) with respect to x

Problem

(∫_^)(1/(7*x3)*d(x))

Solution

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

(∫_^)(1/7*x(−3)*d(x))

2. Factor out the constant coefficient from the integral.

1/7*(∫_^)(x(−3)*d(x))

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

1/7⋅(x(−3+1))/(−3+1)+C

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

1/7⋅(x(−2))/(−2)+C

5. Multiply the fractions and rewrite the expression with a positive exponent in the denominator.

−1/(14*x2)+C

Final Answer

(∫_^)(1/(7*x3)*d(x))=−1/(14*x2)+C

Want more problems? Check here!