You are Here: Home >< Maths

Integration query. watch

1. Is it possible to inegrate the derivatives of the inverse trig functions to obtain a function of x that doesn't actually include the trigonometric terms?

For instance, the derivative of tan-1x is 1/(1+x²). Is it possible to then inegrate 1/(1+x²) using some substitution to obtain a function of x excluding tan-1x?

Because from this you could then find the inverse function which would give you tanx in terms of x and excluding tan. Just a thought.
2. Suppose both f(x) and g(x) differentiate to give you , but and

Therefore we have by construction. Integrate to get where K is a constant. Since we know g(x) we get .

Whatever expression you derive will be but just with a constant added on.

If you mean "Is there a representation of which doesn't actually involve tan?" then yes there is, but it involves complex logorithms, and isn't particularly nice, and as I've just proved, it will be give or take a constant.

does have a rather pleasant Maclaurin series, namely

This gives the exceptionally elegant series for if you put in x=1 as

Unfortunately the rate of convergence is shockingly terrible, needing thousands of terms to get only 3 or 4 decimal places.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 21, 2005
Today on TSR

University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants