作业帮∫sin(7x)cos(10x)dx=?
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∫sin(7x)cos(10x)dx=?
∫sin(7x)cos(10x)dx=?
∫sin(7x)cos(10x)dx=?
原式=1/2∫(sin(17x)+sin(-3x))dx=1/2∫sin(17x)dx-1/2∫sin(3x)dx=-1/34cos(17x)+1/6cos(6x)+C
积化和差得 sin(7x)cos(10x)=1/2*sin(17x)-1/2*sin(3x) ，
所以原式= -1/34*cos(17x)+1/6*cos(3x)+C 。
sin(7x+10x)=sin7xcos10x+cos7xsin10x
sin(7x-10x)=sin7xcos10x-cos7xsin10x
sin17x-sin3x=2sin7xcos10x
∫sin(7x)cos(10x)dx=1/2∫(sin17x-sin3x)dx
=1/2∫sin17xdx-1/2∫sin3xdx
=1/34∫sin17xd17x-1/6∫sin3xd3x
=-1/34∫dcos17x+1/6∫dcos3x
=-1/34cos17x+1/6cos3x+C
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