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Integration of cos2x?
Using chain rule:integral of cos2x dx= 1/2 * sin2x + C
Integration of sin2x?
Integral( sin(2x)dx) = -(cos(2x)/2) + C
What is the integral of 1 divided by the cosine of x with respect to x?
∫ 1/cos(x) dx = ln(sec(x) + tan(x)) + C C is the constant of integration.
What is the derivative of x5lnx?
x5lnx?d/dx (uv)=u*dv/dx+v*du/dxd/dx (x5lnx)=x5*[d/dx(lnx)]+lnx*[d/dx(x5)]-The derivative of lnx is:d/dx(lnu)=(1/u)*[d/dx(u)]d/dx(lnx)=(1/x)*[d/dx(x)]d/dx(lnx)=(1/x)*[1]d/dx(lnx)=(1/x)-The derivative of x5 is:d/dx (xn)=nxn-1d/dx (x5)=5x5-1d/dx (x5)=5x4d/dx (x5lnx)=x5*[1/x]+lnx*[5x4]d/dx (x5lnx)=[x5/x]+5x4lnxd/dx (x5lnx)=x4+5x4lnx
What is the integral of the derivative with respect to x of a function of x with respect to x?
∫ d/dx f(x) dx = f(x) + C C is the constant of integration.
What is integration of x logx dx?
(1/4)x^2(2logx-1) + c
Integration of cos2x?
Using chain rule:integral of cos2x dx= 1/2 * sin2x + C
What are the rules for integration?
There are a lot of rules for integration! Plus a lot of techniques! Here is the power rule as a simple example. int[Xn dx] = (Xn + 1)/(n + 1) + C ( n does not equal - 1 )
What is the integral of 1 divided by x with respect to x?
∫ (1/x) dx = ln(x) + C C is the constant of integration.
What is the anti-derivative of ln x?
The anti-derivative of ( \ln x ) can be found using integration by parts. Let ( u = \ln x ) and ( dv = dx ), then ( du = \frac{1}{x} dx ) and ( v = x ). Applying integration by parts, we get: [ \int \ln x , dx = x \ln x - \int x \cdot \frac{1}{x} , dx = x \ln x - x + C, ] where ( C ) is the constant of integration. Thus, the anti-derivative of ( \ln x ) is ( x \ln x - x + C ).
What is the indefinite answer of 3(3x-1)4 dx?
To find the indefinite integral of the expression (3(3x-1)^4 , dx), we can use the power rule of integration. First, we can factor out the constant 3, then apply the substitution method or directly integrate. The integral becomes: [ \int 3(3x-1)^4 , dx = 3 \cdot \frac{(3x-1)^5}{15} + C = \frac{(3x-1)^5}{5} + C, ] where (C) is the constant of integration.
What is the integral of x diveded by x minus one?
integral x/(x-1) .dx = x - ln(x-1) + c where ln = natural logarithm and c = constant of integration alternatively if you meant: integral x/x - 1 .dx = c
What is the integral of x to the power of n with respect to x?
∫ xn dx = xn+1/(n+1) + C (n ≠-1) C is the constant of integration.
What is the integral of tan cubed x secx dx?
This is a trigonometric integration using trig identities. S tanX^3 secX dX S tanX^2 secX tanX dX S (secX^2 -1) secX tanX dX u = secX du = secX tanX S ( u^2 - 1) du 1/3secX^3 - secX + C
Integration of cos power of 2x plus sin2x dx?
To integrate the expression ( \cos^2(2x) + \sin(2x) , dx ), we can first rewrite ( \cos^2(2x) ) using the Pythagorean identity: ( \cos^2(2x) = \frac{1 + \cos(4x)}{2} ). The integral then becomes: [ \int \left( \frac{1 + \cos(4x)}{2} + \sin(2x) \right) , dx. ] This simplifies to: [ \frac{1}{2} \int (1 + \cos(4x)) , dx + \int \sin(2x) , dx, ] which can be integrated to yield: [ \frac{1}{2} \left( x + \frac{\sin(4x)}{4} \right) - \frac{1}{2} \cos(2x) + C, ] where ( C ) is the constant of integration.
What is the integral of 1 divided by the cosine squared of x with respect to x?
∫ 1/cos2(x) dx = tan(x) + C C is the constant of integration.
What is the integral of 1 divided by the square of the hyperbolic sine of x with respect to x?
∫ 1/sinh2(x) dx = -cotanh + C C is the constant of integration.
