Evaluate the Integral integral of 14x^6 with respect to x

Problem

(∫_^)(14*x6*d(x))

Solution

1. Identify the constant and the power of x in the integrand.

2. Apply the constant multiple rule for integration by moving the constant 14 outside the integral.

14*(∫_^)(x6*d(x))

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

14⋅(x(6+1))/(6+1)+C

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

14⋅(x7)/7+C

5. Divide the constant 14 by 7 to reach the final simplified form.

2*x7+C

Final Answer

(∫_^)(14*x6*d(x))=2*x7+C

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