Evaluate the Integral integral of 1/(6x^5) with respect to x

Problem

(∫_^)(1/(6*x5)*d(x))

Solution

1. Rewrite the integrand by moving the variable to the numerator using the property of exponents 1/(xn)=x(−n)

(∫_^)(1/6*x(−5)*d(x))

2. Apply the constant multiple rule for integration, which allows the constant factor 1/6 to be moved outside the integral.

1/6*(∫_^)(x(−5)*d(x))

3. Apply the power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C where n=−5

1/6⋅(x(−5+1))/(−5+1)+C

4. Simplify the exponent and the denominator.

1/6⋅(x(−4))/(−4)+C

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

−1/(24*x4)+C

Final Answer

(∫_^)(1/(6*x5)*d(x))=−1/(24*x4)+C

Want more problems? Check here!