INTEGRATION – DECOMPOSITION METHOD EXERCISE PROBLEMS

\[\underline{PART\ -\ A}\]
\[1.\ Evaluate: \int(5x^2\ -\ \frac{2}{x^3}\ +\ \frac{1}{x}\ -\ 3)\ dx\ \hspace{18cm}\]
\[2\ Evaluate: \int(x^2 \ +\ cos\ x)\ dx\ \hspace{18cm}\]
\[3\ Evaluate: \int(x^2 \ +\ Sec^2\ x)\ dx\ \hspace{18cm}\]
\[4.\ Evaluate: \int cot^2 x \ dx\ \hspace{18cm}\]
\[\underline{PART\ -\ B}\]
\[5.\ Evaluate: \int(x^2 + x + 1) (x\ +\ 5)\ dx\ \hspace{18cm}\]
\[6.\ Evaluate: \int \frac{sin^2 x}{ 1\ +\ cos x} \ dx\ \hspace{18cm}\]
\[7.\ Evaluate: \int \frac{dx}{1\ -\ sin\ x}\ \hspace{18cm}\]
\[8.\ Evaluate: \int \sqrt{1\ +\ sin\ 2x}\ dx\ \hspace{18cm}\]
\[\underline{PART\ -\ C}\]
\[9.\ Evaluate:\ (i)\ \int (\sqrt{x}\ +\ \frac{1}{\sqrt{x}}) \ dx\ \hspace{2cm}\ (ii)\ \int cos\ x\ cos\ 12\ x\ \ dx\ \hspace{8cm}\]
\[10.\ Evaluate:\ (i)\ \int (x\ -\ 1) (2x\ +\ 3)\ dx\ \hspace{2cm}\ (ii)\ \int 2\ sin\ 3\ x\ cos\ x\ \ dx\ \hspace{8cm}\]
\[11.\ Evaluate:\ (i)\ \int (tan\ x\ +\ cot\ x)^2\ dx\ \hspace{2cm}\ (ii)\ \int sin^3\ x\ dx\ \hspace{8cm}\]
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