Evaluate the Integral integral of 9x^-5 with respect to x

Problem

(∫_^)(9*x(−5)*d(x))

Solution

1. Identify the constant and the power of x in the integrand.

2. Apply the constant multiple rule for integration by moving the constant 9 outside the integral.

9*(∫_^)(x(−5)*d(x))

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

9⋅(x(−5+1))/(−5+1)+C

4. Simplify the exponent and the denominator.

9⋅(x(−4))/(−4)+C

5. Rewrite the expression by combining the constant and the fraction.

−9/4*x(−4)+C

Final Answer

(∫_^)(9*x(−5)*d(x))=−9/(4*x4)+C

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