Find indefinite integrals of the following functions of $x$.
 Question i $\int \! {\left(1+\frac{1}{x}\right)^{2}} \,\mathrm{d}x$ Solution Question ii $\int \! {x\left(3x^{2}+5\right)^{2}} \,\mathrm{d}x$ Solution Question iii $\int \! {2x \sqrt{x}} \,\mathrm{d}x$ Solution Question iv $\int \! {x \sqrt{2x^{2}+4}} \,\mathrm{d}x$ Question v $\int \! {\frac{x^{2}+1}{x^{4}\left(x^{3}+3\right)^{4}}} \,\mathrm{d}x$ Question vi $\int \! {\frac{1}{\sqrt{x}\left(\sqrt{x}+1\right)^{2}}} \,\mathrm{d}x$ Question vii $\int \! {\frac{\left(x^{\frac{2}{3}}+1\right)^{2}}{x^{\frac{1}{3}}}} \,\mathrm{d}x$ Question viii $\int \! {\sin{\left(2x-5\right)}} \,\mathrm{d}x$ Question ix $\int \! {\sec^{2}{4x}} \,\mathrm{d}x$ Question x $\int \! {\tan^{2}{x}} \,\mathrm{d}x$ Question xi $\int \! {\sin{x}\sin{2x}} \,\mathrm{d}x$ Question xii $\int \! {\frac{\sin{x}}{\cos^{3}{x}}} \,\mathrm{d}x$ Question xiii $\int \! {\sin^{2}{x}} \,\mathrm{d}x$ Question xiv $\int \! {\tan^{4}{x}} \,\mathrm{d}x$ Question xv $\int \! {\frac{1}{4+x^{2}}} \,\mathrm{d}x$ Question xvi $\int \! {\frac{1}{\sqrt{4-x^{2}}}} \,\mathrm{d}x$ Question xvii $\int \! {\frac{1}{\sqrt{12-3x^{2}}}} \,\mathrm{d}x$ Question xviii $\int \! {\sqrt{4-9x^{2}}} \,\mathrm{d}x$ Question xix $\int \! {xe^{x^{2}+1}} \,\mathrm{d}x$ Question xx $\int \! {2^{4x}} \,\mathrm{d}x$ Question xxi $\int \! {x \cdot e^{x^{2}}} \,\mathrm{d}x$ Question xxii $\int \! {\frac{1}{10^{3x}}} \,\mathrm{d}x$ Question xxiii $\int \! {\frac{1}{2x-3}} \,\mathrm{d}x$ Question xxiv $\int \! {\frac{x}{2x^{2}-4}} \,\mathrm{d}x$ Question xxv $\int \! {\frac{x^{3}+1}{x\left(x^{3}+4\right)}} \,\mathrm{d}x$ Question xxvi $\int \! {\frac{\sec^{2}{x}}{\tan{x}}} \,\mathrm{d}x$ Question xxvii $\int \! {\cos^{2}{x}\cot{x}} \,\mathrm{d}x$ Question xxviii $\int \! {\tan^{3}{x}} \,\mathrm{d}x$ Question xxix $\int \! {\frac{\sec^{2}{x}}{\sqrt{1+2\tan{x}}}} \,\mathrm{d}x$ Question xxx $\int \! {\frac{1}{x\left(x+1\right)}} \,\mathrm{d}x$ Question xxxi $\int \! {\frac{x-2}{x^{2}-1}} \,\mathrm{d}x$ Question xxxii $\int \! {\frac{3x+4}{\left(x+2\right)^{2}}} \,\mathrm{d}x$ Question xxxiii $\int \! {\frac{1}{x^{2}+2x+5}} \,\mathrm{d}x$ Question xxxiv $\int \! {\frac{a-x}{a^{2}+x^{2}}} \,\mathrm{d}x$ Question xxxv $\int \! {\frac{2\sqrt{2}}{x^{2}+2x-1}} \,\mathrm{d}x$ Question xxxvi $\int \! {\frac{1}{4x^{2}+8x+13}} \,\mathrm{d}x$ Question xxxvii $\int \! {\frac{1}{\sqrt{2x-x^{2}}}} \,\mathrm{d}x$ Question xxxviii $\int \! {\frac{18x}{9x^{2}+6x+4}} \,\mathrm{d}x$ Question xxxix $\int \! {\frac{x^{2}-x+1}{x^{2}\left(x-1\right)}} \,\mathrm{d}x$ Question xxxx $\int \! {\frac{\sin{x}}{1-4\cos^{2}{x}}} \,\mathrm{d}x$ Question xxxxi $\int \! {\frac{1}{\cos^{2}{\left(\frac{1}{2}x\right)}-\sin^{2}{\left(\frac{1}{2}x\right)}}} \,\mathrm{d}x$ Question xxxxii $\int \! {3x \cos{3x}} \,\mathrm{d}x$ Question xxxxiii $\int \! {x \sec^{2}{2x}} \,\mathrm{d}x$ Question xxxxiv $\int \! {\ln{\sqrt{x}}} \,\mathrm{d}x$ Question xxxxv $\int \! {x^{2} e^{-x}} \,\mathrm{d}x$ Question xxxxvi $\int \! {x^{3} \ln{x}} \,\mathrm{d}x$