Calcule: (a) integral x e^x d x (b) integral x sen x d x © integral x^2 e^x d x (d) integral x ln x d x (e) integral ln x d x. MOSTRAR SOLUÇÃO COMPLETAExercícios relacionadosCalcule, utilizando mudança de variáveis, as seguintes integrais: (a) integral raiz3 x-2 d x (b) integral sen^5(x) cos (x) d x © integral 3 x5+6 x^2 d x (d) integral x(1+4 x^2)^2 d x (e) integral e^x raiz1+e^x d x. Defina f(g) e determine os números nos quais f(g) é contínua. (a) f(x) = raiz(x), g(x) = 1 / (x - 2); Calcule: (a) $\int e^{\operatorname{sen} x} \cos x d x$ (b) $\int \frac{e^{t}}{1+e^{2 t}} d t$ (c) $\int \frac{1}{\sqrt{x}+1} d x$ (d) $\int \operatorname{sen}^{2} \theta d \theta$ (e) $\int \frac{1}{y^{2}+6 y+8} d y$ (f) $\int \sqrt{1+\sqrt{x}} d x$.Utilize o T.F.C para calcular as seguintes integrais: (a) integral0^2(t^2+3 t-1) d t (b) integral1^4 1raizx d x © integral1^2 1+xx^3 d x (d) integral0^12 1raiz1-x^2 d x (e) integral1^4 1+xraizx d x (f) integral0^pi3(sen r+sen 2 r) d r (g) integral0^2 2^z d z (h) integral0^1 cosh s d s (i) integral0^pi x e^x d x.