Find h(x)h\left(x\right)h(x) by evaluating the following indefinite integral.h(x)=25x4dxh\left(x\right)=25x^4dxh(x)=25x4dx

h ( x ) = 5 x 5 + C h\left(x\right)=5x^5+C h ( x ) = 5 x 5 + C

Find h ( x ) h\left(x\right) h ( x ) by evaluating the following indefinite integral. h ( x ) = 25 x 4 d x h\left(x\right)=25x^4dx h ( x ) = 25 x 4 d x

this problem, we're asked to find h of x by evaluating the following indefinite integral. So here we have the indefinite integral of 25x to the 4th power, and we're integrating this with respect to x. Now the way that you can solve these types of problems when you have x raised to a power is by taking whatever the exponent is in this function right here, adding 1 to it, and then dividing by that new exponent. So in this case, what I'm going to do is add 1 to the exponent for x to the 4th, then divide everything by that new exponent, which is gonna be 4 plus 1. So we have 25x to the 4 +1, which is the same thing as 25x to the 5th power, and all of that's going to be divided by 4+1, which is 5. So this right here would be the integral for this this function that we have for this integrand. That gives us h of x, and then we have to add the constant of integration, c. Now this could be your final answer right here, but there is a way that we can simplify this to get a little bit better of an answer, and that's by taking this 25 and dividing it by this 5. Doing that is going to give you 5, because because 25 divided by 5 is 5. So we're gonna have 5 x to the 5th power plus c, and this is going to be the fully simplified and best solution for this problem right here. So that's h of x, and that's how you can solve this problem. Hope you found this video helpful. Let's move on and get some more practice.

Find h ( x ) h\left(x\right) h ( x ) by evaluating the following indefinite integral. h ( x ) = 25 x 4 d x h\left(x\right)=25x^4dx h ( x ) = 25 x 4 d x

h ( x ) = 5 x 5 + C h\left(x\right)=5x^5+C h ( x ) = 5 x 5 + C

h ( x ) = 25 x 5 h\left(x\right)=25x^5 h ( x ) = 25 x 5

h ( x ) = 5 x 5 h\left(x\right)=5x^5 h ( x ) = 5 x 5

h ( x ) = 25 x 5 + C h\left(x\right)=25x^5+C h ( x ) = 25 x 5 + C

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

Business Calculus

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

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Multiple Choice

Find $h\left(x\right)$ by evaluating the following indefinite integral.
$h\left(x\right)=25x^4dx$

$h\left(x\right)=25x^5$

$h\left(x\right)=5x^5$

$h\left(x\right)=5x^5+C$

$h\left(x\right)=25x^5+C$

Verified step by step guidance

Step 1: Recognize that the problem involves finding the indefinite integral of the function h(x) = 25x^4. The goal is to apply the power rule for integration.

Step 2: Recall the power rule for integration: ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1. This rule will be applied to the term 25x^4.

Step 3: Apply the power rule to the term 25x^4. Increase the exponent of x by 1 (from 4 to 5) and divide by the new exponent (5). Multiply the result by the constant coefficient 25.

Step 4: Write the result of the integration as h(x) = (25/5)x^5 + C, where C is the constant of integration.

Step 5: Simplify the coefficient (25/5) to get h(x) = 5x^5 + C. This is the final expression for the indefinite integral.

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