-cosine x
.5(x-sin(x)cos(x))+c
∫ sin(x) dx = -cos(x) + CC is the constant of integration.
∫ sinh(x) dx = cosh(x) + C C is the constant of integration.
∫ sin(x)/cos2(x) dx = sec(x) + C C is the constant of integration.
∫ cos(x)/sin2(x) dx = -cosec(x) + C C is the constant of integration.
∫ 1/sin2(x) dx = -cot(x) + CC is the constant of integration.
∫ 1/sin(x) dx = ln(tan(x/2)) + C C is the constant of integration.
∫ 1/sinh2(x) dx = -cotanh + C C is the constant of integration.
Integral from 0 to pi 6sin2xdx: integral of 6sin2xdx (-3)cos2x+c. (-3)cos(2 x pi) - (-3)cos(2 x 0) -3 - -3 0
∫ 1/sinh(x) dx = ln(tanh(x/2)) + C C is the constant of integration.
half range cosine series or sine series is noting but it consderingonly cosine or sine terms in the genralexpansion of fourierseriesfor examplehalf range cosine seriesf(x)=a1/2+sigma n=0to1 an cosnxwhere an=2/c *integral under limits f(x)cosnxand sine series is vice versa
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C