Evaluate the Integral integral of 1/(3x^5) with respect to x

Problem

(∫_^)(1/(3*x5)*d(x))

Solution

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

(∫_^)(1/3*x(−5)*d(x))

2. Apply the constant multiple rule by moving the constant factor outside the integral.

1/3*(∫_^)(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

1/3⋅(x(−5+1))/(−5+1)+C

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

1/3⋅(x(−4))/(−4)+C

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

−1/(12*x4)+C

Final Answer

(∫_^)(1/(3*x5)*d(x))=−1/(12*x4)+C

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