Find the Antiderivative f(x)=5x^4-4x^5

Problem

(∫_^)(5*x4−4*x5*d(x))

Solution

1. Identify the integral of the function ƒ(x)=5*x4−4*x5 to find the antiderivative F(x)

2. Apply the sum rule for integration, which allows the integral to be split into two separate terms.

(∫_^)(5*x4−4*x5*d(x))=(∫_^)(5*x4*d(x))−(∫_^)(4*x5*d(x))

3. Apply the power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1) to each term.

(∫_^)(5*x4*d(x))=5⋅(x5)/5=x5

(∫_^)(4*x5*d(x))=4⋅(x6)/6=(2*x6)/3

4. Combine the results and add the constant of integration C

F(x)=x5−(2*x6)/3+C

Final Answer

(∫_^)(5*x4−4*x5*d(x))=x5−(2*x6)/3+C

Want more problems? Check here!