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.
Chat with our AI personalities
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)