Evaluate the following integrals. e^{2x}\cos(3x)dx

Wierzycaz

Wierzycaz

Answered question

2021-10-03

Evaluate the following integrals.
e2xcos(3x)dx

Answer & Explanation

Elberte

Elberte

Skilled2021-10-04Added 95 answers

Here,
e2xcos(3x)dx=e2xsin3x3sin3x3×2e2xdx
(By the method of by-parts)
=e2xsin3x323e2xsin3xdx
(Again, by the method of by-parts)
=e2xsin3x323[e2x(cos3x)3(cos3x)3×ddx(e2x)dx]
=e2xsin3x323[e2x(cos3x)323e2xcos3xdx]
=e2xsin3x3+29e2xcos3x49e2xcos3xdx
e2xcos3xdx+49e2xcos3xdx=e2xsin3x3+29e2xcos3x
139e2xcos3xdx=e2xsin3x3+29e2xcos3x

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