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By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sqrt(sinx)/(sqrt(sinx) + sqrt(cos x)) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) dx`
Concept: undefined >> undefined
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By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^1 x(1-x)^n dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/4) log (1+ tan x) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_((-pi)/2)^(pi/2) sin^2 x dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_(pi/2)^(pi/2) sin^7 x dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^pi log(1+ cos x) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^4 |x - 1| dx`
Concept: undefined >> undefined
Show that `int_0^a f(x)g (x)dx = 2 int_0^a f(x) dx` if f and g are defined as f(x) = f(a-x) and g(x) + g(a-x) = 4.
Concept: undefined >> undefined
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
Concept: undefined >> undefined
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` dx is ______.
Concept: undefined >> undefined
