Evaluate the Integral integral of 1/(x^9) with respect to x

Problem

(∫_^)(1/(x9)*d(x))

Solution

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

(∫_^)(x(−9)*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(−9+1))/(−9+1)+C

3. Simplify the exponent and the denominator.

(x(−8))/(−8)+C

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

−1/(8*x8)+C

Final Answer

(∫_^)(1/(x9)*d(x))=−1/(8*x8)+C

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