De onbepaalde integraal



is gelijk aan 		A.   − cos + C
B.   − 1op2 cos x + C
C.   −  cos x + C
D.   − cos x + C
E.   \(\ln \frac {1} {\cos^2\frac x2} \) + C
A    B    C    D    E 

[ 6-5577 - op net sinds 15.6.11-(E)-4.11.2023 ]

Translation in   E N G L I S H

Evaluate the
indefinite integral


 A.   − cos + C
B.   − 1op2 cos x + C
C.   −  cos x + C
D.   − cos x + C
E.   \(\ln \frac {1} {\cos^2\frac x2} \) + C

Oplossing - Solution

\( \int \frac{\tan \frac x2}{1+\tan^2 \frac x2}dx = \int (\tan \frac x2\cdot \cos^2 \frac x2)\;dx = \int (\sin \frac x2 \cdot \cos \frac x2) \;dx \\ = \frac12\cdot \int (2\cdot \sin \frac x2 \cdot \cos \frac x2) \;dx = = \frac12 \int \sin x\;dx = -\,\frac12\,\cos x+C \)