\[\begin{array}{l} \smallint \frac{{x{{\rm{e}}^{{{\bf{2}}^x}}}}}{{{{\left( {{\bf{1}} + {\bf{2}}x} \right…
\begin{array}{l} \smallint \sqrt { - \left( {{x^{\bf{2}}} - {\bf{2}}x - {\bf{5}}} \right)} \;{\rm{d}}x\;…
\begin{array}{l} \smallint \sqrt {x\left( {{\bf{4}} - x} \right)} \;\;{\rm{d}}x\;\;\;\;\;\;\;\;\;\;\;\;…
\begin{array}{l} \smallint \frac{{\sqrt {{x^{\bf{2}}} - {\bf{25}}} }}{{{x^{\bf{2}}}}}{\rm{d}}x\\\\ Let …
\begin{array}{l} \smallint \frac{{\sqrt {{\bf{9}} - {x^{\bf{2}}}} }}{{{x^{\bf{2}}}}}{\rm{d}}x\\\\ Let \…
\begin{array}{l} \smallint \frac{{{{\rm{x}}^3}}}{{\sqrt {{{\left( {4{{\rm{x}}^2} + 9} \right)}^3}} }}\;…
\[\begin{array}{l} \smallint \frac{{{\rm{d}}x}}{{\sqrt x + \sqrt[{\bf{3}}]{x}}}\\\\ By\;Substitution\\ …
\begin{array}{l} \smallint \frac{{\bf{1}}}{{{\bf{x}} + {\bf{x}}\sqrt {\bf{x}} }}{\rm{d}}{\bf{x}}\\\\ By\;…
\begin{array}{l} \smallint \frac{{{\bf{1}} + {\bf{sin}}x}}{{{\bf{1}} + {\bf{cos}}x}}{\rm{d}}x\\\\ \small…
\[\begin{array}{l} \smallint \sqrt {\frac{{{\bf{1}} - x}}{{{\bf{1}} + x}}} {\rm{d}}x\\\\ \smallint \sqrt…
\begin{array}{l} \smallint \frac{1}{{1 - cosx}}{\rm{d}}x\\\\ \smallint \frac{1}{{1 - \cos x}}\; * \;\fra…
\[\begin{array}{l} \smallint x{{\rm{e}}^{3x}}{\rm{d}}x\\\\ ByParts\\ Let \Rightarrow u = x\;\;\;\;\;\;\;…
\[\begin{array}{l} \smallint \frac{{lnx}}{{{x^2}}}{\rm{d}}x\\\\ By\;Parts\\ Let \Rightarrow u = \ln x\;…
\begin{array}{l} \smallint \sqrt {cotx} {\rm{d}}x = \\\\ By\;Substitution\\ let \Rightarrow u = \sqrt {\…
\begin{array}{l} \smallint \sqrt {tanx} {\rm{d}}x \;\\\\ BySubstitution\\ z = \sqrt {tanx} \\ {z^2} = t…
\[\smallint \cos \ln x{\rm{d}}x\] \begin{array}{l} By\;Substitution\\ suppose \Rightarrow z = \ln x\\…
\begin{array}{l} \smallint \frac{{\bf{1}}}{{{{\left( {sinx + cosx} \right)}^{\bf{2}}}}}{\rm{d}}x\\\\ \sm…
\[\smallint \sin lnx{\rm{d}}x\] \[\begin{array}{l} By\;Substitution\\ suppose \Rightarrow z = \ln x\…
\[\begin{array}{l} \int \tan ^{-1} x \mathrm{~d} x \\\\ \text { By Parts } \\\\ \text { Let } \Rightarrow …
