Evaluate the Integral integral of 8x^7 with respect to x

Problem

(∫_^)(8*x7*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 8 outside the integral.

(∫_^)(8*x7*d(x))=8*(∫_^)(x7*d(x))

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

8*(∫_^)(x7*d(x))=8⋅(x(7+1))/(7+1)+C

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

8⋅(x8)/8+C

5. Cancel the common factor of 8 in the numerator and denominator.

x8+C

Final Answer

(∫_^)(8*x7*d(x))=x8+C

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