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Antiderivada se denomina tambien integral indefinida <img src="https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4%2Bx%5E3%2B2x%5E2%2Bx" /> <img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3A%28x%5E4%2Bx%5E3%2B2x%5E2%2Bx%29dx" /> <img src="https://tex.z-dn.net/?

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Taylete9904
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Antiderivada se denomina tambien integral indefinida

<img src="https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4%2Bx%5E3%2B2x%5E2%2Bx" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3A%28x%5E4%2Bx%5E3%2B2x%5E2%2Bx%29dx" />

<img src="https://tex.z-dn.net/?f=%3D%5Cint%20%5C%3Ax%5E4dx%2B%5Cint%20%5C%3Ax%5E3dx%2B%5Cint%20%5C%3A2x%5E2dx%2B%5Cint%20%5C%3Axdx" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E4dx%3D%20%5Cfrac%7Bx%5E%7B4%2B1%7D%20%7D%7B4%2B1%7D%3D%20%20%5Cfrac%7Bx%5E%7B5%7D%7D%7B4%7D%20" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3Ax%5E3dx%3D%20%20%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%3D%20%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%20%20" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3A2x%5E2dx%3D%20%5Cfrac%7B2x%5E%7B2%2B1%7D%7D%7B2%2B1%7D%3D%20%5Cfrac%7B2x%5E%7B3%7D%7D%7B3%7D%20%20" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3Axdx%3D%20%5Cfrac%7Bx%5E%7B1%2B1%7D%20%7D%7B1%2B1%7D%3D%20%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B2%7D%20%20" />

Ahora Finalmente agrupamos y le sumamos la constante.

<img src="https://tex.z-dn.net/?f=%5Cint%20%5C%3A%28x%5E4%2Bx%5E3%2B2x%5E2%2Bx%29dx%3D%5Cfrac%7Bx%5E5%7D%7B5%7D%2B%5Cfrac%7Bx%5E4%7D%7B4%7D%2B%5Cfrac%7B2x%5E3%7D%7B3%7D%2B%5Cfrac%7Bx%5E2%7D%7B2%7D%2BC" />.