Solution: Assume $I=\int\left(2 x^{2}+3\right) \sqrt{x+2} d x$ Substituting $x+2=t \Rightarrow d x=d t$ On substituting the values of $x$ in given equation, we obtain $\begin{array}{l} \Rightarrow...
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Exercise 19.10
Solution: Assume $I=\int \frac{2 x-1}{(x-1)^{2}} d x$ Substituting $x-1=t \Rightarrow d x=d t$ On substituting the values of $x$, we get $\Rightarrow \mathrm{I}=\int...
Solution: Assume $\mathrm{I}=\int \frac{\mathrm{x}^{2}}{\sqrt{3 \mathrm{x}+4}} \mathrm{dx}$ Substituting $3 x+4=t \Rightarrow 3 d x=d t$ By substituting the values of $x$, we get $\Rightarrow I=\int...
Solution: Assume $I=\int \frac{x^{2}}{\sqrt{x-1}} d x$ By substituting $x-1=t \Rightarrow d x=d t$ On substituting the values we obtain $\Rightarrow \mathrm{I}=\int...
Solution: Assume $I=\int x^{2} \sqrt{x+2} d x$ By substituting, $x+2=t \Rightarrow d x=d t$ $\begin{array}{l} I=\int(t-2)^{2} \sqrt{t} d t \\ \Rightarrow I=\int\left(t^{2}-4 t+4\right) \sqrt{t} d t...