${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{3x}dx=$

A$)\frac{e^{3x}}{3}(3x-1)C$

D$)\frac{e^{3x}}{3}C$

B$)\frac{e^{3x}}{9}(3x-1)C$

E$)3e^{3x}C$

C$)e^{3x}C$

Difficulty: Medium

Section: $7\mathrm{.}2$

$2.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2{e}^{5x}dx=$

A$)\frac{e^{5x}}{125}(25x^2-10x2)C$

D$)5e^{5x}C$

B$)\frac{x{e}^{5x}}{25}C$

E$),25e^{5x}C$

C$)\frac{e^{5x}}{5}C$

Difficulty: Hard

Section: $7\mathrm{.}2$

$3.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xcos2xdx=$

A$)\frac{xsin2x}{2}C$

D$)\frac{cos2x}{4}\frac{xcos2x}{2}C$

B$)\frac{sin2x}{2}C$

E$),sin2xC$

C$)\frac{cos2x}{4}\frac{xsin2x}{2}C$

Difficulty: Medium

Section: $7\mathrm{.}2{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xsin5xdx=$

A$)\frac{sin5x}{25}-\frac{xcos5x}{5}C$

D$)\frac{sin5x}{5}-\frac{xcos5x}{25}C$

B$)\frac{sin5x}{25}\frac{xcos5x}{5}C$

E$)-\frac{xcos5x}{5}C$

C$)-\frac{sin5x}{25}-\frac{xcos5x}{5}C$

Difficulty: Easy

Section: $7\mathrm{.}2$

$5.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}sin7xdx=$

A$)\frac{2cos7x}{343}\frac{2xsin7x}{49}\frac{x^{2}cos7x}{7}C$

B$)\frac{2cos7x}{343}-\frac{2xsin7x}{49}-\frac{x^{2}cos7x}{7}C$

C$)\frac{2cos7x}{343}\frac{2xsin7x}{49}-\frac{x^{2}cos7x}{7}C$

D$)2cos7x\frac{2xsin7x}{49}-\frac{x^{2}cos7x}{7}C$

E$)2cos7x-\frac{2xsin7x}{49}-\frac{x^{2}cos7x}{7}C$

Difficulty: Hard

Section: $7\mathrm{.}2$

$6.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}9xln(7x)dx=$

A$)\frac{9x^{2}ln(7x)}{2}\frac{9x^2}{4}C$

D$)x^{2}ln(7x)-x^{2}C$

B$)\frac{9x^{2}ln(7x)}{2}-\frac{9x^2}{4}C$

E$)\frac{9x^{2}ln(7x)}{4}-\frac{9x^2}{2}C$

C$)9x^{2}ln(7x)-9x^{2}C$

Difficulty: Medium

Section: $7\mathrm{.}2{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{4x}sin5xdx=$

A$)\frac{e^{4x}}{9}(4sin5x-5cos5x)C$

D$)\frac{e^{4x}}{41}(4sin5x-5cos5x)C$

B$)e^{4x}(4sin5x-5cos5x)C$

E$)\frac{e^{4x}}{18}(4sin5x-5cos5x)C$

C$)e^{4x}(4sin5x5cos5x)C$

Difficulty: Medium

Section: $7\mathrm{.}2$

$8.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{8x}dx=$

A$)\frac{x{e}^{8x}}{8}\frac{e^{8x}}{64}C$

D$)\frac{x{e}^{8x}}{8}-\frac{e^{8x}}{64}C$

B$)\frac{e^{8x}}{8}-\frac{e^{8x}}{64}C$

E$)x{e}^{8x}-e^{8x}C$

C$)\frac{x{e}^{8x}}{64}-\frac{e^{8x}}{8}C$

Difficulty: Medium

Section: $7\mathrm{.}2$

$9.$ Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{sin(2x)}{e^{2x}}dx.$ Very challenging if you do not use tabular method of integration.

Difficulty: Hard

Section: $7\mathrm{.}2$

$10.$ Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ln(99x^2)dx.$

Ans: $xln(99x^2)-2x2ta{n}^{-1}xC$

Difficulty: Medium

Section: $7\mathrm{.}2$

$11.$ Use integration by parts to evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x\sqrt[\phantom{2}]{3x}dx.$

Difficulty: Medium

Section: $7\mathrm{.}2$Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{-2x}dx.$

Ans: $-\frac{x{e}^{-2x}}{2}-\frac{e^{-2x}}{4}C$

Difficulty: Easy

Section: $7\mathrm{.}2$

$13.$ Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{-3x}cos7xdx.$

Difficulty: Hard

Section: $7\mathrm{.}2$

$14.$Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}l{n}^{2}9xdx.$

Difficulty: Hard

Section: $7\mathrm{.}2$

$15.$ Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{4x}dx.$

Difficulty: Easy

Section: $7\mathrm{.}2$

$16.$ Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xsinxdx.$

Difficulty: Medium

Section: $7\mathrm{.}2$