STANDARD INTEGRALS (Excercise Problems)

\[\underline{PART\ -\ A}\]

\[1.\ Evaluate\ :\ \int \frac{dx}{9\ +\ x^2}\ \hspace{15cm}\]

\[2.\ Evaluate\ :\ \int \frac{dx}{3\ +\ 2 x^2}\ \hspace{15cm}\]

\[\underline{PART\ -\ B}\]

\[3.\ Evaluate\ :\ \int \frac{dx}{{\sqrt{36 – x^2}}}\ \hspace{15cm}\]

\[4.\ Evaluate\ :\ \int \frac{dx}{4x^2\ -\ 49}\ \hspace{15cm}\]

\[\underline{PART\ -\ C}\]

\[5.\ Evaluate:\ \hspace{2cm}\ (i)\ \int\ \frac{dx}{16\ +\ x^2}\ \hspace{2cm}\ (ii)\ \int\frac{dx}{{\sqrt{4\ -\ (x\ +\ 1)^2}}}\ \hspace{10cm}\]

\[6.\ Evaluate:\ \hspace{2cm}\ (i)\ \int\ \frac{dx}{64\ -\ x^2}\ \hspace{2cm}\ (ii)\ \int\frac{dx}{{\sqrt{36\ -\ (5x\ +\ 1)^2}}}\ \hspace{10cm}\]

\[7.\ Evaluate:\ \hspace{2cm}\ (i)\ \int\ \frac{dx}{25\ -\ 9x^2}\ \hspace{2cm}\ (ii)\ \int\frac{dx}{(2x + 3)^2\ +\ 9}\ \hspace{10cm}\]

\[8.\ Evaluate:\ \int\ \frac{dx}{3\ -\ 2x\ -\ x^2}\ \hspace{15cm}\]