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3 Answers
- 1 decade ago
Since you're integrating with respect to x, then you can treat y as a constant:
tan(xy) * dx =>
sin(xy) * dx / cos(xy)
u = cos(xy)
du = -y * sin(xy) * dx
Now we're integrating:
(-1 / y) * du / u =>
(-1 / y) * ln( |u| ) + C =>
(-1 / y) * ln( |cos(xy)| ) + C
- RayLv 71 decade ago
-(1/y) ln [cos(xy)] + C
Remember that y is an independent variable since we are integrating with respect to x.
- ?Lv 61 decade ago
∫ tan(xy) dx
Note that y is behaving like a constant.
∫ [sin(xy)] / [cos(xy)] dx
u = cos(xy)
du = -ysin(xy) dx
dx = -1/(ysin(xy)) du
(-1/y) ∫ 1/u du
(-1/y) ln|u|
(-1/y)ln|cos(xy)| + C
Done!
