Integrals Test ...

If $$\int _{ log2 }^{ x }{ \dfrac { dx }{ \sqrt { { e }^{ x }-1 }  }  } =\dfrac { \pi  }{ 6 } ,$$then x is equal to _________.

If $$\int { x\sin { x }  } dx=-x\cos { x } +\alpha $$, then $$\alpha$$ is equal to

What is $$\displaystyle \int \dfrac{dx}{2x^2 - 2x + 1}$$ equal to ?

Select and write the most appropriate answer from the given alternatives for question :
If $$\displaystyle \int^k_0 4x^3dx=16$$, then the value of $$k$$ is _____.

Evaluate $$\displaystyle\int^4_1x\sqrt{x}dx$$

Evaluate : $$\displaystyle\int^1_0\dfrac{dx}{\sqrt{5x+3}}$$

Evaluate : $$\displaystyle\int^2_0\sqrt{6x+4}dx$$

Evaluate $$\displaystyle\int^2_0\dfrac{dx}{\sqrt{4-x^2}}$$

Evaluate $$\displaystyle\int^1_0\dfrac{x^3}{(1+x^8)}dx$$

Evaluate $$\displaystyle\int^{\sqrt{8}}_{\sqrt{3}}x\sqrt{1+x^2}dx$$