(1/4)x^2(2logx-1) + c
d/dx ( log x) = 1/x
To integrate ( x \sec x ), you can use integration by parts. Let ( u = x ) and ( dv = \sec x , dx ). Then, ( du = dx ) and ( v = \ln |\sec x + \tan x| ). Applying the integration by parts formula, you get: [ \int x \sec x , dx = x \ln |\sec x + \tan x| - \int \ln |\sec x + \tan x| , dx + C ] where ( C ) is the constant of integration. The second integral may require further techniques to evaluate.
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 ).
-logx=21.1 logx=-21.1 e^-21.1=x
To integrate ( x \tan(x) ), we can use integration by parts. Let ( u = x ) and ( dv = \tan(x) , dx ). This gives ( du = dx ) and ( v = -\ln|\cos(x)| ). Applying the integration by parts formula ( \int u , dv = uv - \int v , du ), we obtain: [ \int x \tan(x) , dx = -x \ln|\cos(x)| + \int \ln|\cos(x)| , dx + C ] The integral ( \int \ln|\cos(x)| , dx ) does not have a simple closed form, so the final result may be expressed in terms of this integral along with the logarithmic term.
d/dx ( log x) = 1/x
X(logX-1) + C
To integrate ( x \sec x ), you can use integration by parts. Let ( u = x ) and ( dv = \sec x , dx ). Then, ( du = dx ) and ( v = \ln |\sec x + \tan x| ). Applying the integration by parts formula, you get: [ \int x \sec x , dx = x \ln |\sec x + \tan x| - \int \ln |\sec x + \tan x| , dx + C ] where ( C ) is the constant of integration. The second integral may require further techniques to evaluate.
logx^2=2 2logx=2 logx=1 10^1=x x=10
The integral of f'(x) = 1 is f(x) = x + c
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 ).
∫ d/dx f(x) dx = f(x) + C C is the constant of integration.
-logx=21.1 logx=-21.1 e^-21.1=x
y=logx y=10 logx= 10 10logx = 10log1 logx = log1 x = 1 //NajN
To integrate ( x \tan(x) ), we can use integration by parts. Let ( u = x ) and ( dv = \tan(x) , dx ). This gives ( du = dx ) and ( v = -\ln|\cos(x)| ). Applying the integration by parts formula ( \int u , dv = uv - \int v , du ), we obtain: [ \int x \tan(x) , dx = -x \ln|\cos(x)| + \int \ln|\cos(x)| , dx + C ] The integral ( \int \ln|\cos(x)| , dx ) does not have a simple closed form, so the final result may be expressed in terms of this integral along with the logarithmic term.
∫ sin(x) dx = -cos(x) + CC is the constant of integration.
∫ cos(x) dx = sin(x) + CC is the constant of integration.