- #1

- 363

- 79

- Homework Statement
- $$\int (\frac{1}{cos^2x\cdot tan^3x})dx$$

- Relevant Equations
- none

That's my attempt:

$$\int (\frac{1}{cos^2x\cdot tan^3x})dx = \int (\frac{1}{cos^2x}\cdot tan^{-3}x) dx$$

Now, being ##\frac{1}{cos^2x}## the derivative of ##tanx##, the integral gets:

$$-\frac{1}{2tan^2x}+c$$

But there is something wrong... what?

$$\int (\frac{1}{cos^2x\cdot tan^3x})dx = \int (\frac{1}{cos^2x}\cdot tan^{-3}x) dx$$

Now, being ##\frac{1}{cos^2x}## the derivative of ##tanx##, the integral gets:

$$-\frac{1}{2tan^2x}+c$$

But there is something wrong... what?