Calcule: (a) integral x e^x d x (b) integral x^2 e^x d x © integral x ln x d x (d) integral x^2 ln x d x (e) integral x^2 sin x d x MOSTRAR SOLUÇÃO COMPLETAExercícios relacionadosCalcule: (a) $\int_{0}^{1} x e^{x} d x$ (b) $\int_{0}^{\pi} x^{3} \cos \left(x^{2}\right) d x$Calcule, utilizando mudança de variáveis, as seguintes integrais: (a) integral raiz3 x-2 d x (b) integral 11+9 x^2 d x © integral sen^5(x) cos (x) d x (d) integral x(1+4 x^2)^2 d x (e) integral e^x raiz1+e^x d x (f) integral 2 x+3raiz1-4 x^2 d x (g) integral 1raiz1-(ln x)^2 d x. Calcule: (a) integral e^sin x cos x d x (b) integral e^t1+e^2 t d t © integral 1raizx+1 d x (d) integral sin^2 theta d theta (e) integral raizcos (3 t) sin(3 t) d t (f) integral 1y^2+6 y+8 d y (g) integral (2 x + 1) e^x^2 e^x d x Derive a função f(x)=(1+x^(-1))^2