U-Substituion: Evaluate the following integrals.

\(\displaystyle{ \int (1-2x)^5   \, \,  dx }\)     Solution

\( \displaystyle{\int \frac{x}{x+1}  \, \,  dx}\)   solution

\( \displaystyle{\int x \, \cos (1+x^2)   \, \,  dx}\)     Solution

 \( \displaystyle{\int \frac{x^2} {1+x^3}  \, \,   dx}\)  Solution

 \( \displaystyle{\int \frac{(\ln x)^4}{4x}  \, \,   dx}\)     Solution  

\(\displaystyle{\int \frac{x^2-4}{x^3-12x+6} \, dx}\)  solution

\( \displaystyle{\int \frac{\sin (\ln x)}{x}  \, \,   dx}\)   Solution  

\( \displaystyle{\int \cot \theta  \, \,  d\theta}\)   Solution

\( \displaystyle{\int \tan x   \, \,  dx}\)   Solution

\( \displaystyle{\int x^2 \cos (x^3)   \, \,  dx}\)   Solution

\( \displaystyle{\int (t-2)\sqrt{3t^2-12t} \, \,  dt}\)   Solution

\( \displaystyle{\int \left(1-\frac{1}{x}\right)\, \sin\left(x - \ln x \right)}\, dx\)     solution

\(\displaystyle{\int e^{x^5} x^4\, dx}\)  solution

\(\displaystyle{\int \frac{x^8}{\sqrt{x^9-7}}\, dx}\)   solution

\(\displaystyle{\int \frac{e^{5x}}{2+e^{5x}} \, dx}\)  solution

\( \displaystyle{\int \frac{1}{x \ln x}  \, \,  dx}\)  Solution

\( \displaystyle{\int x \,\sqrt{1-x^2}   \, \,  dx}\)  Solution

\( \displaystyle{\int \sin\theta \, (1+ \cos \theta)^3   \, \,  d\theta}\)  Solution

\(\displaystyle{ \int_{-1}^1  x\,(x^2+1)^2  \, \,  dx}\)  Solution 

\(\displaystyle{ \int_0^1  x \, \sqrt{5x^2+4}  \, \, dx}\)  Solution 

 \(\displaystyle{ \int_1^2  \frac{x}{(x^2+3)^2}  \, \,   dx}\)   Solution 

\( \displaystyle{\int_0^1 \frac{x+2}{\sqrt{x^2+4x}}  \, \,    dx}\)    Solution

  \( \displaystyle{\int_0^4 \frac{e^{\sqrt{x}}} {\sqrt{x}}   \, \,   dx} \)   Solution

  \( \displaystyle{\int_0^1 \frac{\tan^{-1} t} {1+t^2}  \, \,  dt}\)   Solution