Exercise:
Berechne die folgen uneigentlichen Integrale sofern diese existieren und gib jeweils den korrespondieren Definitionsbereich an falls dies verlangt wird. abcliste abc _^infty fracu^+ddu abc _^ sqrtxddxquad D_f? abc _^infty fracy+ddyquad D_f? abc _^ fracpisqrts^-dds abc _^infty fract+t^ddt abcliste

Solution:
abcliste abc _^infty fracu^+ddu lim_lambda rightarrow infty_^lambda fracu^+ddu lim_lambda rightarrow inftyleftfracarctan fracuright_^lambda lim_lambda rightarrow infty leftfracarctan fraclambda - leftfracarctan rightright frac fracpi fracpi abc _^ sqrtxddx lim_lambda rightarrow _lambda^ sqrtxddx lim_lambda rightarrow leftfracx^fracright_lambda^ lim_lambda rightarrow ^+leftfrac-leftfraclambda^fracrightright frac- frac &Rightarrow D_fmathbbR_^+ abc _^infty fracy+ddy lim_lambda rightarrow infty _^lambda fracy+ddy lim_lambda rightarrow inftyleftln |y+|right_^lambda lim_lambda rightarrow infty left ln |lambda +|-leftln ||rightright infty textexistiert nicht &Rightarrow D_fmathbbRbackslash - abc _^ fracpisqrts^-dds pi lim_lambda rightarrow ^+_lambda^ fracsqrts^-dds pi lim_lambda rightarrow ^+leftln |s+sqrts^-|right_lambda^ pi lim_lambda rightarrow ^+leftln |+sqrt|-leftln |lambda +sqrtlambda^-|rightright pi leftln |+sqrt|-ln ||right pi ln +sqrt &Rightarrow D_fxin mathbbR| |x| abc _^infty fract+t^ddt lim_lambda rightarrow infty _^lambda fract+t^ddt lim_lambda rightarrow infty left-fract^-fract^right_^lambda lim_lambda rightarrow infty left-fraclambda^-fraclambda^-left-frac-fracrightright -left-frac-fracright frac+frac frac frac abcliste