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tanxsec^2x
Solving integrals/ tanxsec^2x

Integral of tanxsec^2x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫0π4tan⁡(x)sec⁡2(x) dx\int\limits_{0}^{\frac{\pi}{4}} \tan{\left(x \right)} \sec^{2}{\left(x \right)}\, dx 
Integral(tan(x)*sec(x)^2, (x, 0, pi/4))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Let u=tan⁡(x)u = \tan{\left(x \right)}.

      Then let du=(tan⁡2(x)+1)dxdu = \left(\tan^{2}{\left(x \right)} + 1\right) dx and substitute dudu:

      ∫u du\int u\, du

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u du=u22\int u\, du = \frac{u^{2}}{2}

      Now substitute uu back in:

      tan⁡2(x)2\frac{\tan^{2}{\left(x \right)}}{2}

    Method #2

    1. Let u=sec⁡(x)u = \sec{\left(x \right)}.

      Then let du=tan⁡(x)sec⁡(x)dxdu = \tan{\left(x \right)} \sec{\left(x \right)} dx and substitute dudu:

      ∫u du\int u\, du

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u du=u22\int u\, du = \frac{u^{2}}{2}

      Now substitute uu back in:

      sec⁡2(x)2\frac{\sec^{2}{\left(x \right)}}{2}

  2. Add the constant of integration:

    tan⁡2(x)2+constant\frac{\tan^{2}{\left(x \right)}}{2}+ \mathrm{constant}

The answer is:

tan⁡2(x)2+constant\frac{\tan^{2}{\left(x \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | tan(x)*sec (x) dx = C + -------
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∫tan⁡(x)sec⁡2(x) dx=C+tan⁡2(x)2\int \tan{\left(x \right)} \sec^{2}{\left(x \right)}\, dx = C + \frac{\tan^{2}{\left(x \right)}}{2}
Simplify
The graph
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.7504
Plot the graph f(x)
The answer [src] 
1/2
12\frac{1}{2} 
=
= 
1/2
12\frac{1}{2} 
1/2
Numerical answer [src] 
0.5
0.5
The graph
Integral of tanxsec^2x dx

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

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