∫▒〖(x+1)(x^2 〗+2x+5)^12 dx
não consegui resolver esta integral
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Oi. Espero que ajude em algo:
![\int {[(x+1)(x^2)]+(2x+5)^{12}} \, dx \\ \\ \int {[x^3+x^2]+(2x+5)^{12}} \, dx \\ \\ \int {x^3} \, dx+\int {x^2} \, dx+\int {(2x+5)^{12}} \, dx \ \ \ u=2x+5 \ \ \ du=2.dx\\ \\ \frac{x^{3+1}}{3+1}+ \frac{x^{2+1}}{2+1}+ \frac{1}{2} \int {u^{12}} \, du \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{1}{2} \frac{u^{12+1}}{12+1} +C \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{1}{2} \frac{u^{13}}{13} +C \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{(2x+5)^{13}}{26} +C](https://tex.z-dn.net/?f=+%5Cint+%7B%5B%28x%2B1%29%28x%5E2%29%5D%2B%282x%2B5%29%5E%7B12%7D%7D+%5C%2C+dx++%5C%5C++%5C%5C++%5Cint+%7B%5Bx%5E3%2Bx%5E2%5D%2B%282x%2B5%29%5E%7B12%7D%7D+%5C%2C+dx+%5C%5C++%5C%5C+%5Cint+%7Bx%5E3%7D+%5C%2C+dx%2B%5Cint+%7Bx%5E2%7D+%5C%2C+dx%2B%5Cint+%7B%282x%2B5%29%5E%7B12%7D%7D+%5C%2C+dx++%5C+%5C+%5C+u%3D2x%2B5+%5C+%5C+%5C+du%3D2.dx%5C%5C++%5C%5C++%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%2B+%5Cfrac%7Bx%5E%7B2%2B1%7D%7D%7B2%2B1%7D%2B+%5Cfrac%7B1%7D%7B2%7D+%5Cint+%7Bu%5E%7B12%7D%7D+%5C%2C+du+%5C%5C++%5C%5C++%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%2B+%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B+%5Cfrac%7B1%7D%7B2%7D++%5Cfrac%7Bu%5E%7B12%2B1%7D%7D%7B12%2B1%7D++%2BC+%5C%5C++%5C%5C++%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%2B+%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B+%5Cfrac%7B1%7D%7B2%7D++%5Cfrac%7Bu%5E%7B13%7D%7D%7B13%7D++%2BC++%5C%5C++%5C%5C++%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%2B+%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B++%5Cfrac%7B%282x%2B5%29%5E%7B13%7D%7D%7B26%7D++%2BC+ "\int {[(x+1)(x^2)]+(2x+5)^{12}} \, dx \\ \\ \int {[x^3+x^2]+(2x+5)^{12}} \, dx \\ \\ \int {x^3} \, dx+\int {x^2} \, dx+\int {(2x+5)^{12}} \, dx \ \ \ u=2x+5 \ \ \ du=2.dx\\ \\ \frac{x^{3+1}}{3+1}+ \frac{x^{2+1}}{2+1}+ \frac{1}{2} \int {u^{12}} \, du \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{1}{2} \frac{u^{12+1}}{12+1} +C \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{1}{2} \frac{u^{13}}{13} +C \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{(2x+5)^{13}}{26} +C")
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