Integrate Number Work For Free with DocHub and make the most of your documents

Aug 6th, 2022
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  1. Pick any available method to add a document, bring one from the cloud, drag and drop your file, or add it via link, etc.
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  4. Find the option to Integrate Number Work For Free and apply it to your document. Select the undo option to discard this action.
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How to Integrate Number Work For Free

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in this video im going to show you how to integrate using u-substitution so were going to focus on the definite integrals how can we find the anti-derivative of 4x times x squared plus five raised to the third power so what do we need to do we need to define two things we need to identify the u variable and d u now whatever you select u to be du has to be the derivative if we select u to be 4x the derivative will be 4 and thats not going to get rid of x squared plus 5. we need to change all of the x variables into u variables now if we make u equal to x squared plus 5 d u is going to be 2x which can cancel the x and 4x and thats what we want to do so lets set u equal to x squared plus five d u is going to be 2x but times dx so what im going to do now is solve for dx in this equation so if i divide both sides by 2x dx is equal to du divided by 2x now what you need to do is replace this with u and replace the dx with du over 2x and it will all work out so lets go ahead and do tha

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Answer: The integral of the given constant expression 3 dx is equal to 3x + C, where C is an arbitrary constant. Lets understand the solution in detail. Now, we know that the indefinite integral of any constant a is ax + C, where C is an arbitrary constant. Hence, similarly, 3 dx = 3x + C.
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The integration of uv formula is a special rule of integration by parts. Here we integrate the product of two functions. If u(x) and v(x) are the two functions and are of the form u dv, then the Integration of uv formula is given as: uv dx = u v dx - (u v dx) dx.
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Integration is the reverse of differentiation. So the integral of 2 can be 2x + 3, 2x + 5, 2x, etc. For this reason, when we integrate, we have to add a constant. So the integral of 2 is 2x + c, where c is a constant.

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