Integral of tg²x dx

The solution

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$$\int\limits_{0}^{1} \tan^{2}{\left(x \right)}\, dx$$

Integral(tan(x)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\tan^{2}{\left(x \right)} = \sec^{2}{\left(x \right)} - 1$
Integrate term-by-term:
1. $\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $- x + \tan{\left(x \right)}$
Add the constant of integration:

$- x + \tan{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- x + \tan{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
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 | tan (x) dx = C - x + tan(x)
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$$\tan x-x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     sin(1)
-1 + ------
     cos(1)

$$\tan 1-1$$

     sin(1)
-1 + ------
     cos(1)

$$-1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$

Simplify

Numerical answer [src]

0.557407724654902

0.557407724654902

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

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Identical expressions

Integral of tg²x dx

Limits of integration:

The graph:

Piecewise:

The solution