Exercícios 1.2.2 Exercícios
Tecnologia 1.2.9.
Use o Sage para calcular as integrais propostas nos exercícios e confira com as suas respostas.
Calcular as integrais seguintes usando o método da substituição.
1.
\(\displaystyle\int (2x^2+2x-3)^{10}(2x+1) dx\)
2.
\(\displaystyle\int (x^3-2)^{1/7}x^2 dx\)
3.
\(\displaystyle\int \frac{x dx}{\sqrt[5]{x^2-1}}\)
4.
\(\displaystyle\int 5x\sqrt{4-3x^2} dx\)
5.
\(\displaystyle\int \sqrt{x^2+2x^4} dx\)
6.
\(\displaystyle\int (e^{2t}+2)^{1/3}e^{2t} dt\)
7.
\(\displaystyle\int \frac{e^t dt}{e^t+4}\)
8.
\(\displaystyle\int \frac{e^{1/x}+2}{x^2} dx\)
9.
\(\displaystyle\int \operatorname{tg} x \sec^2 x dx\)
10.
\(\displaystyle\int \operatorname{sen}^4 x \cos x dx\)
11.
\(\displaystyle\int \frac{\operatorname{sen} x}{\cos^5 x} dx\)
12.
\(\displaystyle\int \frac{2\operatorname{sen} x - 5\cos x}{\cos x} dx\)
13.
\(\displaystyle\int e^x \cos(2e^x) dx\)
14.
\(\displaystyle\int \frac{x}{2} \cos x^2 dx\)
15.
\(\displaystyle\int \operatorname{sen}(5\theta - \pi) d\theta\)
16.
\(\displaystyle\int \frac{\operatorname{arc\,sen} y}{2\sqrt{1-y^2}} dy\)
17.
\(\displaystyle\int \frac{2\sec^2 \theta}{a + b\operatorname{tg} \theta} d\theta\)
18.
\(\displaystyle\int \frac{dx}{16+x^2}\)
19.
\(\displaystyle\int \frac{dy}{y^2-4y+4}\)
20.
\(\displaystyle\int \sqrt[3]{\operatorname{sen} \theta} \cos \theta d\theta\)
21.
\(\displaystyle\int \frac{\ln x^2}{x} dx\)
22.
\(\displaystyle\int (e^{ax} + e^{-ax})^2 dx\)
23.
\(\displaystyle\int \sqrt{3t^4+t^2} dt\)
24.
\(\displaystyle\int \frac{4dx}{4x^2+20x+34}\)
25.
\(\displaystyle\int \frac{3 dx}{x^2-4x+1}\)
26.
\(\displaystyle\int \frac{e^x dx}{e^{2x}+16}\)
27.
\(\displaystyle\int \frac{\sqrt{x+3}}{x-1} dx\)
28.
\(\displaystyle\int \frac{3 dx}{x \ln^2 3x}\)
29.
\(\displaystyle\int (\operatorname{sen} 4x + \cos 2\pi) dx\)
30.
\(\displaystyle\int 2^{x^2+1} x dx\)
31.
\(\displaystyle\int x e^{3x^2} dx\)
32.
\(\displaystyle\int \frac{dt}{(2+t)^2}\)
33.
\(\displaystyle\int \frac{dt}{t \ln t}\)
34.
\(\displaystyle\int 8x\sqrt{1-2x^2} dx\)
35.
\(\displaystyle\int (e^{2x}+2)^5 e^{2x} dx\)
36.
\(\displaystyle\int \frac{4t dt}{\sqrt{4t^2+5}}\)
37.
\(\displaystyle\int \frac{\cos x}{3 - \operatorname{sen} x} dx\)
38.
\(\displaystyle\int \frac{dv}{\sqrt{v}(1+\sqrt{v})^5}\)
39.
\(\displaystyle\int x^2\sqrt{1+x} dx\)
40.
\(\displaystyle\int x^4 e^{-x^5} dx\)
41.
\(\displaystyle\int t \cos t^2 dt\)
42.
\(\displaystyle\int 8x^2\sqrt{6x^3+5} dx\)
43.
\(\displaystyle\int \operatorname{sen}^{1/2} 2\theta \cos 2\theta d\theta\)
44.
\(\displaystyle\displaystyle\int \sec^2(5x+3) dx\)
45.
\(\displaystyle\int \frac{\operatorname{sen} \theta d\theta}{(5-\cos \theta)^3}\)
46.
\(\displaystyle\int \operatorname{cotg} u du\)
47.
\(\displaystyle\int (1+e^{-at})^{3/2} e^{-at} dt, a > 0\)
48.
\(\displaystyle\int \frac{\cos \sqrt{x}}{\sqrt{x}} dx\)
49.
\(\displaystyle\int t\sqrt{t-4} dt\)
50.
\(\displaystyle\int x^2(\operatorname{sen} 2x^3 + 4x) dx\)
