I on this indefinite integral

[Oomair]

Homework Statement

ok I am given this problem

indef. int (1+tan^2*5x)dx i need to use the u subsitution method to find the answer but i cannot seem to find what to subsitute

the worksheet says the answer is " one-fifth*tan5x+C

Homework Equations

The Attempt at a Solution

 

[Gib Z]

The using the Pythagorean Identity $$1+ \tan^2 x = \sec^2 x$$, we can change your problem to:
$$\int \sec^2 (5x) dx$$. then let u= 5x. du= 5 dx, or dx = (1/5) du.

We can take constants out of the integral, so it becomes $$\frac{1}{5} \int \sec^2 u du$$. You should know that the derivative of tan x is sec^2 x, so the integral is $$\frac{1}{5} \tan u + C = \frac{1}{5} \tan (5x) + C$$

 

[Oomair]

thanks for the help, i got the trig idenity, but the problem was that i was letting u=sec^25x