To integrate tan(x), you must break up tangent into sine over cosine, with that being done, all you have is a u-substitution with the cosine. This should give:
int(tan(x)dx)=int(sin(x)/cos(x)dx)=int(-(1/u)*du)=-ln|u|+C=-ln|cos(x)|+C u=cos(x) du=-sin(x)dx
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Integration for inverse tangent of square x
sin(x) = tan(x) when x equal 0
It is a function which maps the tangent ratio - any real value - to an angle in the range (-pi/2, pi/2) radians. Or (-90, 90) degrees.If tan(x) = y then x is the inverse tangent of y.It is also known as "arc tangent", and spreadsheets, such as Excel, use "atan" for this function.Warning:1/tangent = cotangent is the reciprocal, NOT the inverse.
The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X. The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.
_____ 1 x (x+4) (x-3)