Evaluate the Integral integral of 1/(x^4) with respect to x

Problem

(∫_^)(1/(x4)*d(x))

Solution

1. Rewrite the integrand using a negative exponent to prepare for the power rule.

(∫_^)(x(−4)*d(x))

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

(x(−4+1))/(−4+1)+C

3. Simplify the exponent and the denominator.

(x(−3))/(−3)+C

4. Rewrite the expression using a positive exponent by moving the variable back to the denominator.

−1/(3*x3)+C

Final Answer

(∫_^)(1/(x4)*d(x))=−1/(3*x3)+C

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