Evaluate the Integral integral of 1/(7x^6) with respect to x

Problem

(∫_^)(1/(7*x6)*d(x))

Solution

1. Rewrite the integrand by moving the variable to the numerator using a negative exponent.

(∫_^)(1/7*x(−6)*d(x))

2. Apply the constant multiple rule to move the constant factor outside the integral.

1/7*(∫_^)(x(−6)*d(x))

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

1/7⋅(x(−6+1))/(−6+1)+C

4. Simplify the exponent and the denominator.

1/7⋅(x(−5))/(−5)+C

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

−1/(35*x5)+C

Final Answer

(∫_^)(1/(7*x6)*d(x))=−1/(35*x5)+C

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