Evaluate the Integral integral of 1/(4x^3) with respect to x

Problem

(∫_^)(1/(4*x3)*d(x))

Solution

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

(∫_^)(1/4*x(−3)*d(x))

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

1/4*(∫_^)(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

1/4⋅(x(−3+1))/(−3+1)+C

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

1/4⋅(x(−2))/(−2)+C

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

−1/(8*x2)+C

Final Answer

(∫_^)(1/(4*x3)*d(x))=−1/(8*x2)+C

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