اسئلة تكامل

\[\begin{array}{l}
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Evaluate \\
\left( i \right)\,\,\,\,\,\int {{x^2}\ln x} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\int {x\sin 3x} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\,\,\,\left( {iii} \right)\,\,\,\,\,\int {{x^2}\cos \pi x} \,dx\,\,\,\,\,\,\,,\, \\
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\left( {iv} \right)\,\,\,\,\,\int {\ln \left| {3x + 2} \right|} \,dx\,\,\,\,\,\,\,,\,\,\,\,\left( v \right)\,\,\,\,\,\int {\arctan 6x} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\,\,\left( {vi} \right)\,\,\,\,\,\int {x{{\sec }^2}2x} \,dx\,\,\,\,\,\,\,,\, \\
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\left( {vii} \right)\,\,\,\,\,\int {{{\left( {\ln x} \right)}^2}} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {viii} \right)\,\,\,\,\,\int {{e^{2x}}\sin 5x} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {ix} \right)\,\,\,\,\,\int {x\cosh x} \,dx\,\,\,\,\,\,\,,\, \\
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\left( x \right)\,\,\,\,\int_0^{1/2} {{{\cos }^{ - 1}}x} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xi} \right)\,\,\,\,\,\int {\sin x\ln \left| {\cos x} \right|} \,dx\,\,\,\,,\,\,\,\,\left( {xii} \right)\,\,\,\,\,\int\limits_1^2 {{x^4}{{\left( {\ln x} \right)}^2}} \,dx\,\,\,\,,\, \\
\left( {xiii} \right)*\,\int {\sin \sqrt x } \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xiv} \right)*\,\,\int\limits_{\sqrt {\pi /2} }^{\sqrt \pi } {{\theta ^3}\cos {\theta ^2}} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xv} \right)*\,\,\int {x\ln \left( {x + 1} \right)} \,dx\, \\
\,\,\,\,\,\,,\, \\
\left( {xvi} \right)\,\,\int {\left( {5x + 4} \right)} \ln x\,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xvii} \right)\,\,\,\,\,\int {{x^3}\sqrt {{x^2} + 1} } \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xviii} \right)\,\,\,\,\,\int {\underline {{{\left( {\ln x} \right)}^3}} } \,dx\, \\
\,\,\,\,\,\,,\, \\
\left( {xiv} \right)\,\int {{{\sec }^3}x} \,\,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xx} \right)\,\,\,\,\,\int {{x^3}\sqrt {{x^2} + 1} } \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xxi} \right)\,\,\,\,\,\int {{{\tan }^{ - 1}}} 2x\,dx\,\,\,\,\,\,\,,\, \\
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\left( {xxii} \right)\,\,\int {\ln \left( {{x^2} + 3} \right)} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xxiii} \right)\,\,\,\,\,\int {{x^3}\sin x} \,dx\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\left( {xxiv} \right)\,\,\,\,\,\int {x{{\tan }^{ - 1}}} x\,dx \\
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\end{array}\]