The Web site integrals.wolfram.com gives the following:
integral of sin2x/x = (1/2) (log x - Ci(2 x))
Ci is the cosine integral, a special function. Look at the site for a more detailed description.
What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.
The Web site integrals.wolfram.com gives the following:
integral of sin2x/x = (1/2) (log x - Ci(2 x))
Ci is the cosine integral, a special function. Look at the site for a more detailed description.
What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.
The Web site integrals.wolfram.com gives the following:
integral of sin2x/x = (1/2) (log x - Ci(2 x))
Ci is the cosine integral, a special function. Look at the site for a more detailed description.
What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.
The Web site integrals.wolfram.com gives the following:
integral of sin2x/x = (1/2) (log x - Ci(2 x))
Ci is the cosine integral, a special function. Look at the site for a more detailed description.
What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.
The Web site integrals.wolfram.com gives the following:
integral of sin2x/x = (1/2) (log x - Ci(2 x))
Ci is the cosine integral, a special function. Look at the site for a more detailed description.
What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.
Integral of 1 is x Integral of tan(2x) = Integral of [sin(2x)/cos(2x)] =-ln (cos(2x)) /2 Integral of tan^2 (2x) = Integral of sec^2(2x)-1 = tan(2x)/2 - x Combining all, Integral of 1 plus tan(2x) plus tan squared 2x is x-ln(cos(2x))/2 +tan(2x)/2 - x + C = -ln (cos(2x))/2 + tan(2x)/2 + C
-cos x + Constant
No.
Ah, secant, annoying as always. Why don't we use its definition as 1/cos x and csc as 1/sin x? We will do that Also, please write down the equation, there is at least TWO different equations you are talking about. x^n means x to the power of n 1/(sin x) ^2 is csc squared x, it's actually csc x all squared 1/(cos x) ^2 in the same manner.
sin2x + c
.5(x-sin(x)cos(x))+c
∫ sin(x)/cos2(x) dx = sec(x) + C C is the constant of integration.
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
22
sin integral is -cos This is so because the derivative of cos x = -sin x
Sin squared is equal to 1 - cos squared.
Integral of 1 is x Integral of tan(2x) = Integral of [sin(2x)/cos(2x)] =-ln (cos(2x)) /2 Integral of tan^2 (2x) = Integral of sec^2(2x)-1 = tan(2x)/2 - x Combining all, Integral of 1 plus tan(2x) plus tan squared 2x is x-ln(cos(2x))/2 +tan(2x)/2 - x + C = -ln (cos(2x))/2 + tan(2x)/2 + C
Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
Sin squared, cos squared...you removed the x in the equation.
The Integral diverges. It has singularities whenever sin(x)+cos(x)=0. Singularities do not necessarily imply that the integral goes to infinity, but that is the case here, since the indefinite integral is x/2 + 1/2 Log[-Cos[x] - Sin[x]]. Obviously this diverges when evaluated at zero and 2pi.
sin squared
sin cubed + cos cubed (sin + cos)( sin squared - sin.cos + cos squared) (sin + cos)(1 + sin.cos)