What is int tan 1 secx tanx equal to ........

Mathematics (NDA) Integration

What is ∫ tan^-1 ( secx + tanx ) equal to?

πx / 4 + x² / 4 + c

πx / 2 + x² / 4 + c

πx / 4 + πx² / 4 + c

πx / 4 - x² / 4 + c

∫ tan^-1 [ 1 / cosx + sinx / cosx]dx = ∫ tan^-1 [ 1+sinx / cosx ] dx

= ∫ tan^-1 ( 1+cos( π / 2 −x) / sin( π / 2 −x) ) dx

=∫ tan^-1 [ 2cosx²( π / 4 − x / 2 ) / 2 sin( π / 4 − x / 2 )cos( π / 4 − x / 2 ) ] dx

= ∫ tan^-1 [cot ( π / 4 − x / 2 )] dx

=∫ tan^-1 [tan { π/2 −( π / 4 − x / 2 )}] dx

= ∫[ π / 4 + x / 2 ] dx

= πx / 4 + x²/ 4 + c

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