Find the Antiderivative f(x)=18x^5

Problem

(∫_^)(18*x5*d(x))

Solution

1. Identify the function to be integrated, which is ƒ(x)=18*x5

2. Apply the constant multiple rule for integration, which allows the constant 18 to be moved outside the integral.

18*(∫_^)(x5*d(x))

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

18⋅(x(5+1))/(5+1)+C

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

18⋅(x6)/6+C

5. Divide the constant 18 by 6 to find the final coefficient.

3*x6+C

Final Answer

(∫_^)(18*x5*d(x))=3*x6+C

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