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Calculus Level 3

∫ 0 π 4 ln ⁡ ( 1 + tan ⁡ θ ) d θ = ? \large \int_0^{\frac\pi4} \ln(1+\tan\theta) \, d\theta = \ ?

π 16 ln ⁡ ( 2 ) \frac\pi{16} \ln(2) π 2 ln ⁡ ( 2 ) \frac\pi2 \ln(2) π 8 ln ⁡ ( 2 ) \frac\pi8 \ln(2) π 4 ln ⁡ ( 2 ) \frac\pi4 \ln(2)

Shashank Rustagi by Shashank Rustagi , 24, India

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1 solution

Shashank Rustagi
Jul 3, 2015

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Is it possible to use the same technique if the integral is ∫ 0 π 4 ln ⁡ ( 1 + tan ⁡ 2 θ ) d θ \displaystyle \int_0^{\frac\pi4} \ln(1 + \tan^2\theta)\, d\theta instead?

maybe no . No it is not possible

Shashank Rustagi - 5 years, 11 months ago

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