Cálculo NII: notas de aula

1.

1. \(\displaystyle \int \frac{dx}{x^3}\)
2. \(\displaystyle \int \left(9t^2 + \frac{1}{\sqrt{t^3}}\right) dt\)
3. \(\displaystyle \int (ax^4 + bx^3 + 3c) dx\)
4. \(\displaystyle \int (\frac{1}{\sqrt{x}} + \frac{x\sqrt{x}}{3}) dx\)
5. \(\displaystyle \int (2x^2 - 3)^2 dx\)
6. \(\displaystyle \int \frac{dx}{sen^2x}\)
7. \(\displaystyle \int (\sqrt{2y} - \frac{1}{\sqrt{2y}}) dy\)
8. \(\displaystyle \int \frac{\sqrt{2}dt}{3t^2 + 3}\)
9. \(\displaystyle \int x^3\sqrt{x} dx\)
10. \(\displaystyle \int \frac{x^5 + 2x^2 - 1}{x^4} dx\)

2.

1. \(\displaystyle \int \frac{x^2}{x^2 + 1} dx\)
2. \(\displaystyle \int \frac{x^2 + 1}{x^2} dx\)
3. \(\displaystyle \int \frac{sen\,x}{cos^2x} dx\)
4. \(\displaystyle \int \sqrt{\frac{9}{1 - x^2}} dx\)
5. \(\displaystyle \int \sqrt{\frac{4}{x^4 - x^2}} dx\)
6. \(\displaystyle \int \frac{8x^4 - 9x^3 + 6x^2 - 2x + 1}{x^2} dx\)
7. \(\displaystyle \int (\frac{e^t}{2} + \sqrt{t} + \frac{1}{t}) dt\)
8. \(\displaystyle \int cos\,\theta \cdot tg\,\theta \, d\theta\)
9. \(\displaystyle \int (e^x - e^{-x}) dx\)
10. \(\displaystyle \int (t + \sqrt{t} + \sqrt[3]{t} + \sqrt[4]{t} + \sqrt[5]{t}) dt\)
11. \(\displaystyle \int \frac{x^{-1/3} - 5}{x} dx\)
12. \(\displaystyle \int (2^t - \sqrt{2}e^t + cosh\,t) dt\)
13. \(\displaystyle \int sec^2x(cos^3x + 1) dx\)
14. \(\int \frac{dx}{(ax)^2 + a^2}\text{,}\) onde \(a \ne 0\) é constante.
15. \(\displaystyle \int \frac{x^2 - 1}{x^2 + 1} dx\)
16. \(\displaystyle \int \sqrt[3]{8(t - 2)^6(t + \frac{1}{2})^3} dt\)
17. \(\displaystyle \int (e^t - \sqrt[4]{16t} + \frac{3}{t^3}) dt\)
18. \(\displaystyle \int \frac{ln\,x}{x\,ln\,x^2} dx\)
19. \(\displaystyle \int tg^2x \cdot cosec^2x \, dx\)
20. \(\displaystyle \int (x - 1)^2 (x + 1)^2 dx\)
21. \(\int \frac{dt}{(n - 1/2)t^n}\text{,}\) onde \(n \in \mathbb{Z}\text{.}\)

3.