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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
Integration formula of second puc syllabus?
The integration formulas covered in the second PUC syllabus primarily include basic integration techniques such as integration of power functions, trigonometric functions, exponential functions, and logarithmic functions. Key formulas include ∫ x^n dx = (x^(n+1))/(n+1) + C for n ≠ -1, ∫ sin(x) dx = -cos(x) + C, and ∫ e^x dx = e^x + C. Additionally, students learn about integration by substitution and integration by parts. Understanding these fundamental formulas is essential for solving various problems in calculus.
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 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
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.
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.
