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4sin-3x-e-4x-4-




Question Number 68316 by 9102176137086 last updated on 08/Sep/19
∫(4sin 3x+(e^(4x) /4))
$$\int\left(\mathrm{4sin}\:\mathrm{3}{x}+\frac{{e}^{\mathrm{4}{x}} }{\mathrm{4}}\right) \\ $$
Commented by mathmax by abdo last updated on 08/Sep/19
=4∫ sin(3x)dx +(1/4)∫ e^(4x) dx +c  =−(4/3)cos(3x) +(1/(16))e^(4x)  +c .
$$=\mathrm{4}\int\:{sin}\left(\mathrm{3}{x}\right){dx}\:+\frac{\mathrm{1}}{\mathrm{4}}\int\:{e}^{\mathrm{4}{x}} {dx}\:+{c} \\ $$$$=−\frac{\mathrm{4}}{\mathrm{3}}{cos}\left(\mathrm{3}{x}\right)\:+\frac{\mathrm{1}}{\mathrm{16}}{e}^{\mathrm{4}{x}} \:+{c}\:. \\ $$

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