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integrate-2-4x-dx-




Question Number 21772 by j.masanja06@gmail.com last updated on 03/Oct/17
integrate  ∫2^(4x) dx
integrate24xdx
Answered by mrW1 last updated on 03/Oct/17
∫2^(4x) dx  =(1/4)∫2^(4x) d(4x)  =(1/4)∫2^t dt  with t=4x  =(1/4)∫e^(tln 2)  dt  =(1/(4ln 2))∫e^(tln 2)  d(tln 2)  =(1/(4ln 2))∫e^u  du  with u=tln 2=ln 2^t =ln 2^(4x)   =(1/(4ln 2))×e^u +C  =(1/(4ln 2))×e^(ln 2^(4x) ) +C  =(2^(4x) /(4ln 2))+C
24xdx=1424xd(4x)=142tdtwitht=4x=14etln2dt=14ln2etln2d(tln2)=14ln2euduwithu=tln2=ln2t=ln24x=14ln2×eu+C=14ln2×eln24x+C=24x4ln2+C
Answered by sma3l2996 last updated on 03/Oct/17
=∫e^(4xln2) dx=(2^(4x) /(4ln2))+C
=e4xln2dx=24x4ln2+C

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