MvCalc60

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\int _{0}^{a}\int _{0}^{x}[e^{{x+y+z}}]_{{0}}^{{y+x}}dydx\,

\int _{0}^{a}\int _{0}^{x}[e^{{2x+2y}}-e^{{x+y}}]dydx\,

=\int _{0}^{a}[{\frac  {e^{{2x+2y}}}{2}}-e^{{x+y}}]_{0}^{x}\,

=\int _{0}^{a}[{\frac  {e^{{4x}}}{2}}-e^{{2x}}-{\frac  {e^{{2x}}}{2}}+e^{x}]dx\,

=[{\frac  {e^{{4x}}}{8}}-{\frac  {e^{{2x}}}{2}}-{\frac  {e^{{2x}}}{4}}+e^{x}]_{0}^{a}\,

={\frac  {e^{{4a}}}{8}}-{\frac  {e^{{2a}}}{2}}-{\frac  {e^{{2a}}}{4}}+e^{a}-{\frac  {1}{8}}+{\frac  {1}{2}}+{\frac  {1}{4}}-1\,

={\frac  {e^{{4a}}}{8}}-{\frac  {3}{4}}e^{{2a}}+e^{a}-{\frac  {3}{8}}\,

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