α এর মান কত হলে ∫₁^α  {2+xln(x²+5)}dx +∫₁^α {3-xln(x²+5)}dx=30 

$\int_{1}^{a}\left\{2+x \ln \left(x^{2}+5\right)\right\} d x+\int_{1}^{a}\left\{3-x \ln \left(x^{2}+5\right)\right\} d x=30$

$\begin{array}{l} \Rightarrow \int_{1}^{\alpha} 2 d x+\int_{1}^{\alpha} x \ln \left(x^{2}+5\right) d x+\int_{1}^{\alpha} 3 d x-\int_{1}^{\alpha} x \ln \left(x^{2}+5\right) d x=30 \\ \Rightarrow \int_{1}^{\alpha} 2 d x+\int_{1}^{\alpha} 3 d x=30 \\ \Rightarrow[2 x]_{1}^{\alpha}+[3 x]_{1}^{\alpha}=30 \\ \Rightarrow 2 \alpha-2+3 \alpha-3=30 \\ \Rightarrow 5 \alpha-5=30 \\ \Rightarrow 5 \alpha=35 \\ \Rightarrow \alpha=7 \end{array}$