Log1+x Integration

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$1. \displaystyle{\int x^n dx = \dfrac{x^{n + 1}}{n + 1}} \\[3mm] \displaystyle{\int (ax + b)^n = \dfrac{1}{a} \dfrac{(ax + b)^{n + 1}}{n + 1}, n \neq -1} \\[3mm] 2.\displaystyle{\int \dfrac{1}{x} dx = \log x} \\[3mm] \displaystyle{\int \dfrac{1}{ax + b} dx = \dfrac{1}{a} \log (ax + b)} \\[3mm] 3. \displaystyle{\int e^x dx = e^x} \\[3mm] \displaystyle{\int e^{ax + b} dx = \dfrac{1}{a}e^{ax + b}} \\[3mm] 4. \displaystyle{\int a^x dx = \dfrac{a^x}{\log_e a}} \\[3mm] \displaystyle{\int a^{px + q} dx = \dfrac{1}{p} \dfrac{a^{px + q}}{\log_w a}}$

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$\\\int \left(\log \left(\log \left(x\right)\right)+\frac{1}{\left(\log \left(x\right)\right)^2}\right)dx\\put\:\log \left(x\right)=t\\x=e^t\Rightarrow \:\:\\dx=e^tdt\\\Rightarrow \int \:e^t\left(\log \left(t\right)+\frac{1}{^{t^2}}\right)dt\:\\\Rightarrow \int \:\:e^t\left(\log \:\left(t\right)+\frac{1}{t}-\frac{1}{t}+\frac{1}{^{t^2}}\right)dt\\\Rightarrow \int \:e^t\left(\log \left(t\right)+\frac{1}{t}\right)dt-\int \:e^t\left(\frac{1}{t}+\left(-\frac{1}{t^2}\right)\right)dt\:\:\:\:\\now\:apply\\\int \:e^x\left(f\left(x\right)+f'\left(x\right)\right)dx=e^xf\left(x\right)+c$

Evaluate Integrate Log Log X 1 Log X 2 Dx