Exercício
$\int_{0.618}^0\left(\frac{-10x^2+5x+5}{2\sqrt{1-x-x^2}}\right)dx$
Solução explicada passo a passo
Aprenda online a resolver problemas passo a passo. int((-10.0x^2+5x+5)/(2(1-x-x^2)^(1/2)))dx&0.618&0. Aplicamos a regra: \int_{a}^{b} xdx=-\int_{b}^{a} xdx, onde a=0.618, b=0 e x=\frac{-10x^2+5x+5}{2\sqrt{1-x-x^2}}. Aplicamos a regra: \int\frac{a}{bc}dx=\frac{1}{c}\int\frac{a}{b}dx, onde a=-10x^2+5x+5, b=\sqrt{1-x-x^2} e c=2. Aplicamos a regra: \frac{a}{b}c=\frac{ca}{b}, onde a=1, b=2, c=-1, a/b=\frac{1}{2} e ca/b=- \left(\frac{1}{2}\right)\int\frac{-10x^2+5x+5}{\sqrt{1-x-x^2}}dx. Reescreva a expressão \frac{-10x^2+5x+5}{\sqrt{1-x-x^2}} que está dentro da integral na forma fatorada.
int((-10.0x^2+5x+5)/(2(1-x-x^2)^(1/2)))dx&0.618&0
Resposta final para o problema
$\frac{25}{8}\arcsin\left(\frac{2\left(0.618+\frac{1}{2}\right)}{\sqrt{5}}\right)-\frac{5}{2}\cdot \left(0.618+\frac{1}{2}\right)\sqrt{- \left(0.618+\frac{1}{2}\right)^2+\frac{5}{4}}+\frac{5}{4}\arcsin\left(\frac{0.618+\frac{1}{2}}{\sqrt{5}}\right)+\frac{15}{2}\sqrt{- \left(0.618+\frac{1}{2}\right)^2+\frac{5}{4}}+\frac{5}{4}\arcsin\left(\frac{2\left(0.618+\frac{1}{2}\right)}{\sqrt{5}}\right)-\frac{5}{2}\arcsin\left(\frac{2\left(0.618+\frac{1}{2}\right)}{\sqrt{5}}\right)-\left(\frac{25}{8}\arcsin\left(\frac{2\left(0+\frac{1}{2}\right)}{\sqrt{5}}\right)-\frac{5}{2}\cdot \left(0+\frac{1}{2}\right)\sqrt{- \left(0+\frac{1}{2}\right)^2+\frac{5}{4}}+\frac{5}{4}\arcsin\left(\frac{0+\frac{1}{2}}{\sqrt{5}}\right)+\frac{15}{2}\sqrt{- \left(0+\frac{1}{2}\right)^2+\frac{5}{4}}+\frac{5}{4}\arcsin\left(\frac{2\left(0+\frac{1}{2}\right)}{\sqrt{5}}\right)-\frac{5}{2}\arcsin\left(\frac{2\left(0+\frac{1}{2}\right)}{\sqrt{5}}\right)\right)$