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What is antiderivative y=((tgx)^2+(tgx)^4)?
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You need to evaluate the indefinite integral of the given function, such that:
`int f(x)dx = int (tan^2 x + tan^4 x)dx`
You need to factor out `tan^2 x` , such that:
`int f(x)dx = int tan^2 x(1 + tan^2 x)dx`
You should use the following trigonometric identity, such that:
`1 + tan^2 x = 1/(cos^2 x)`
Replacing `1/(cos^2 x)` for `1 +` `tan^2 x` yields:
`int f(x)dx = int tan^2 x*(dx)/(cos^2 x)`
You should come up with the following substitution, such that:
`tan x = t => (dx)/(cos^2 x) = dt`
Replacing the variable yields:
`int t^2 dt = t^3/3 + c`
Replacing back `tan x` for t yields:
`int (tan^2 x + tan^4 x)dx= (tan^3 x)/3 + c`
Hence, evaluating the anti-derivative of the given function, yields `int (tan^2 x + tan^4 x)dx = (tan^3 x)/3 + c`
Posted by sciencesolve on July 8, 2013 at 4:04 PM (Answer #1)
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