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Evaluate : int (1)/(" cos (x+a) . sin (x+b)") " dx " |
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Answer» SOLUTION :`int (1)/(" cos (x+a) . SIN (x+b)") " dx "` `=(1)/(" cos(a-b)") int(1)/("cos (x_+a) . sin (x+b)")"dx "` `=(1)/(cos(a-b)).int{{"cos(a-b) -(x+b)}}/(cos(x+a).sin(x+b)) dx` `cos (x+b) cos (x+b)` `=(1)/("cos(a-b)") int (+"sin (x+a)sin (x+b))/(cos (x+a) sin (x+b)) dx` `=(1)/(cos(a-b)) int{(cos(x+a)cos(x+b))/(cos(x+a)sin(x+b))` `=(sin (x+a) sin(x+b))/(cos(x+a)sin(x+b))} dx` `=(1)/(cos (a-b)) int {COT(x+b)+tan(x+a)}dx` `=(1)/(cos(a-b)) [log |sin(x+b)| +log |sec (x+a)|] +c.` |
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