Integrals Test ...

Let $$F(x)=f(x)+f\left ( \dfrac{1}{x} \right )$$, where $$f(x)=\int_{l}^{x}\dfrac{logt}{l+t}dt$$. Then $$F(e)$$ equals

For x > 0, let f(x) = $$\displaystyle \int_{1}^{x}{ \frac{log t}{1 + t}} dt $$. Then f(x) + f$$\displaystyle \left( \frac{1}{x} \right)$$ is equal to:

The value of $$\displaystyle\int^{2\pi}_{0}\dfrac{x\sin^8x}{\sin^8x+\cos^8x}dx$$ is equal to?

The integral $$\displaystyle\int^{{\pi}/{4}}_{{\pi}/{12}}\frac{8\cos 2x}{(\tan x+\cot x)^3}dx$$ equals?

The value of $$\displaystyle \int_{0}^{1}\frac{8\log(1+\mathrm{x})}{1+\mathrm{x}^{2}}$$ dx is 

If $$\displaystyle\int \dfrac{\cos x \, dx}{\sin^3x(1+\sin^6x)^{2/3}} = f(x)(1 + \sin^6x)^{1/\alpha} + c$$
Where $$c$$ is a constant of integration, then $$\lambda f\left(\dfrac{\pi}{3}\right)$$ is equal to:

The following integral $$\displaystyle \int_{\pi/4}^{\pi/2} (2 cosec  x)^{17}dx$$ is equal to

The value of $$g\displaystyle \left ( \frac{1}{2} \right )$$ is?

The value of the integral $$\displaystyle \int_0^1 \dfrac{x^{\alpha}-1}{\log x}dx$$ is

$$\int _{ 0 }^{ \pi  }{ \cfrac { xdx }{ 4\cos ^{ 2 }{ x } +9\sin ^{ 2 }{ x }  }  } =$$