A.  \(\boldsymbol{\frac {x^2} {2}\sin\,(x^2)+C }\)
B.  \(\boldsymbol{-\,\frac 12 \sin\,(x^2)+C }\)
C.  \(\boldsymbol{\frac 13\sin\,(x^3)+C }\)
D.  \(\boldsymbol{-\,\frac 13\sin\,(x^3)+C}\)
E.  \(\boldsymbol{\frac 12 \sin\,(x^2)+C }\)
                 

[ 6-2472 - op net sinds 21.2.15-(E)-30.10.2023 ]

Translation in   E N G L I S H

A.   \(\boldsymbol{\frac {x^2} {2}\sin\,(x^2)+C }\)
B.   \(\boldsymbol{-\,\frac 12 \sin\,(x^2)+C }\)
C.   \(\boldsymbol{\frac 13\sin\,(x^3)+C }\)
D.   \(\boldsymbol{-\,\frac 13\sin\,(x^3)+C}\)
E.   \(\boldsymbol{\frac 12 \sin\,(x^2)+C }\)

Oplossing - Solution

∫x.cos x² dx = ∫ cos x² d (½x²) = ½ ∫ cos x² d x² = ½ sin x² + C
(zonder die expliciet te schrijven zit hier de substitutie t = x² in verborgen)