Find the Integral 7/(x^4)

Problem

(∫_^)(7/(x4)*d(x))

Solution

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

(∫_^)(7*x(−4)*d(x))

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

7⋅(x(−4+1))/(−4+1)+C

3. Simplify the exponent and the denominator.

7⋅(x(−3))/(−3)+C

4. Rewrite the expression by moving the negative exponent back to the denominator and simplifying the fraction.

−7/(3*x3)+C

Final Answer

(∫_^)(7/(x4)*d(x))=−7/(3*x3)+C

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