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Evaluate the indefinite integral

0 votes

∫e^(4x)*sin(7x)dx?

asked May 27, 2013 in CALCULUS by chrisgirl Apprentice

1 Answer

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Let y = ʃe4x  sin(7x)dx = ʃsin(7x) e4x dx

The integration product formula

ʃuv = uʃv - ʃu'ʃv

                          = sin7x ʃe4x - ʃ7cos7xʃe4xxdx

                          = sin7x×e4x / 4 - ʃ7cos7xe4x / 4dx

                         = sin7x×e4x / 4 - 7 / 4[cos7x × e4x  / 4 - ʃ-7sin7x×e4x / 4 dx]

                    y = sin7x ×e4x / 4 - 7 / 16cos7x×e4x -49 / 16[ʃsin7x×e4x dx]

                   y = sin7x ×e4x / 4 - 7 / 16cos7x×e4x - 49 / 16[y]

                  y = sin7x ×e4x / 4 - 7 / 16cos7x×e4x - 49y / 16

                 y + 49y / 16 = sin7x ×e4x / 4 - 7 / 16cos7x×e4x

                      65y / 16 = sin7x ×e4x / 4 - 7 / 16cos7x×e4x

                          y = 16 / 65[sin7x ×e4x / 4 - 7 / 16cos7x×e4x]

                          y = 1 / 65[4sin7x ×e4x  - 7 cos7x×e4x]

                          y = e4x / 65[4sin7x - 7cos7x].

answered Jun 4, 2013 by diane Scholar

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