${\displaystyle \underset{0}{\overset{0}{}}}{x}^5(a^2-x^2{)}^{4}dx.$

${\displaystyle \underset{0}{\overset{1}{}}}{x}^4\sqrt[\phantom{2}]{1-x^4}dx.$

$.$

${\displaystyle \underset{0}{\overset{a}{}}}{x}^4(a^2-x^2{)}^{2}dx.$

${\displaystyle \underset{0}{\overset{\frac{}{6}}{}}}co{s}^{4}3d.$ Put $3=x.$

Ans. $\frac{35r}{768}.$

${\displaystyle \underset{0}{\overset{4}{}}}si{n}^6(\frac{1}{2}y)co{s}^7(\frac{1}{y}ydy).$

${\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}si{n}^{2}4yco{s}^{2}2ydy.$

${\displaystyle \underset{0}{\overset{1}{}}}\sqrt[\phantom{2}]{1-\sqrt[\phantom{2}]{u}}du.$ Put $u=si{n}^{4}x.$

$In$ Exs. $29-60,$ evaluate the given definite integral $by$ any available device.

${\displaystyle \underset{0}{\overset{1}{}}}\frac{dx}{\sqrt[\phantom{2}]{1+8x}}$

Ans. $\frac{1}{2}.$

${\displaystyle \underset{-1}{\overset{0}{}}}\frac{x^{2}dx}{(1-x^2)i}.$

Ans. $\frac{2-\sqrt[\phantom{2}]{2}}{3}.$

${\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}si{n}^{2}ydy.$

Ans $\frac{s}{2}.$

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{2}ydy.$

Ans. $$

${\displaystyle \underset{1}{\overset{4}{}}}\sqrt[\phantom{2}]{\sqrt[\phantom{2}]{x}-1}dx.$

Ans. $1\frac{39}{8}.$

${\displaystyle \underset{0}{\overset{}{}}}co{s}^{2}d.$

Ans. $0.$

${\displaystyle \underset{0}{\overset{1}{}}}\frac{x^{2}dx}{(x+1{)}^4}.$

Ans. $\frac{1}{8}.$

${\displaystyle \underset{0}{\overset{ln2}{}}}\frac{e^{2x}dx}{\sqrt[\phantom{2}]{1+e^2}}.$

Ans. $\frac{2\sqrt[\phantom{2}]{2}}{3}.$

${\displaystyle \underset{0}{\overset{1}{}}}$Arcsinydy. Ans. $\frac{1}{4}-1.$

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}xcos2xdx.$

Ans. $-\frac{1}{8}.$

${\displaystyle \underset{1}{\overset{\sqrt[\phantom{2}]{2}}{}}}\frac{dx}{x^2\sqrt[\phantom{2}]{4-x^2}}.$

Ans. $\frac{\sqrt[\phantom{2}]{3}-1}{4}.$

${\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}si{n}^{2}xdx.$

Ans. $\frac{4-3\sqrt[\phantom{2}]{3}}{24}.$

${\displaystyle \underset{0}{\overset{ln2}{}}}x{e}^{-2}dx.$

Ans. $\frac{1}{8}(1-ln2).$

${\displaystyle \underset{1}{\overset{2}{}}}\frac{xdx}{x+1}$

Ans. $1-ln(\frac{3}{8})$

${\displaystyle \underset{0}{\overset{1}{}}}\frac{(5-x)dx}{4x^2+1}.$

Ans. $\frac{5x-ln2}{8}$

${\displaystyle \underset{1}{\overset{\sqrt[\phantom{2}]{8}}{}}}$Arctanxdx.

Ans. $-\frac{1}{2}ln2+\frac{}{12}(4\sqrt[\phantom{2}]{3}-3)$

${\displaystyle \underset{0}{\overset{1}{}}}\frac{ydy}{(1+y{)}^4}.$