Evaluate the integral ${\int }_1^4(1+\ln x)x^{x}dx$.

Evaluate the definite integral ${\int }_1^e\frac{dx}{x\sqrt{{\ln }^{2}x+9}}$. Express your answer in terms of logarithms. 

Compute $\int \frac{dx}{27-x^2}$, for $x>3\sqrt{3}$.

Evaluate the integral: $\int \frac{6x}{3x^2+5}dx$

Let $h\left(x\right)=\frac{3-x}{x}$. Are there any numbers such that ${\int }_{3-c}^{3+c}h\left(x\right)dx=0$?