Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of 1÷x
- Integral of √(1+sinx)
- Integral of a^x*e^x
-
Integral of exp(7*x)*sin(x)
-
Identical expressions
- (exp^(two *x- two *y)-exp(x-y))/(one +exp^y)
- ( exponent of to the power of (2 multiply by x minus 2 multiply by y) minus exponent of (x minus y)) divide by (1 plus exponent of to the power of y)
- ( exponent of to the power of (two multiply by x minus two multiply by y) minus exponent of (x minus y)) divide by (one plus exponent of to the power of y)
- (exp(2*x-2*y)-exp(x-y))/(1+expy)
- exp2*x-2*y-expx-y/1+expy
- (exp^(2x-2y)-exp(x-y))/(1+exp^y)
- (exp(2x-2y)-exp(x-y))/(1+expy)
- exp2x-2y-expx-y/1+expy
- exp^2x-2y-expx-y/1+exp^y
- (exp^(2*x-2*y)-exp(x-y)) divide by (1+exp^y)
- (exp^(2*x-2*y)-exp(x-y))/(1+exp^y)dx
-
Similar expressions
- (exp^(2*x+2*y)-exp(x-y))/(1+exp^y)
- (exp^(2*x-2*y)+exp(x-y))/(1+exp^y)
- (exp^(2*x-2*y)-exp(x+y))/(1+exp^y)
- (exp^(2*x-2*y)-exp(x-y))/(1-exp^y)
Integral of (exp^(2*x-2*y)-exp(x-y))/(1+exp^y) dy
The solution
You have entered
[src]
x / | | 2*x - 2*y x - y | E - e | ------------------- dy | y | 1 + E | / 0
$$\int\limits_{0}^{x} \frac{e^{2 x - 2 y} - e^{x - y}}{e^{y} + 1}\, dy$$
Integral((E^(2*x - 2*y) - exp(x - y))/(1 + E^y), (y, 0, x))
The answer
[src]
2*x / x 2*x\ -x 1 x e / x 2*x\ \2*e + 2*e /*e / x\ x / x\ x / x\ - - - e - ---- + x*\e + e / + ------------------- + \1 + e /*e *log(2) - \1 + e /*e *log\1 + e / 2 2 2
$$x \left(e^{2 x} + e^{x}\right) - \left(e^{x} + 1\right) e^{x} \log{\left(e^{x} + 1 \right)} + \left(e^{x} + 1\right) e^{x} \log{\left(2 \right)} + \frac{\left(2 e^{2 x} + 2 e^{x}\right) e^{- x}}{2} - \frac{e^{2 x}}{2} - e^{x} - \frac{1}{2}$$
=
=
2*x / x 2*x\ -x 1 x e / x 2*x\ \2*e + 2*e /*e / x\ x / x\ x / x\ - - - e - ---- + x*\e + e / + ------------------- + \1 + e /*e *log(2) - \1 + e /*e *log\1 + e / 2 2 2
$$x \left(e^{2 x} + e^{x}\right) - \left(e^{x} + 1\right) e^{x} \log{\left(e^{x} + 1 \right)} + \left(e^{x} + 1\right) e^{x} \log{\left(2 \right)} + \frac{\left(2 e^{2 x} + 2 e^{x}\right) e^{- x}}{2} - \frac{e^{2 x}}{2} - e^{x} - \frac{1}{2}$$
-1/2 - exp(x) - exp(2*x)/2 + x*(exp(x) + exp(2*x)) + (2*exp(x) + 2*exp(2*x))*exp(-x)/2 + (1 + exp(x))*exp(x)*log(2) - (1 + exp(x))*exp(x)*log(1 + exp(x))
Use the examples entering the upper and lower limits of integration.