Question 1

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;u%5C&space;dv \int u\ dv)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;u%5C&space;dv)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?uv&space;-&space;%5Cint&space;v%5C&space;du uv - \int v\ du)](http://www.codecogs.com/eqnedit.php?latex=uv&space;-&space;%5Cint&space;v%5C&space;du)

Question 2

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;u%5E%7Bn%7D%5C&space;du \int u^{n}\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;u%5E%7Bn%7D%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7Bu%5E%7Bn&plus;1%7D%7D%7Bn&space;&plus;&space;1%7D&space;&plus;&space;C%5C&space;%5C&space;%5C&space;%5C&space;%5C&space;n%5Cneq&space;1 \frac{u^{n+1}}{n + 1} + C\ \ \ \ \ n
eq 1)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Bu%5E%7Bn&plus;1%7D%7D%7Bn&space;&plus;&space;1%7D&space;&plus;&space;C%5C&space;%5C&space;%5C&space;%5C&space;%5C&space;n%5Cneq&space;1)

Question 3

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;%5Cfrac%7Bdu%7D%7Bu%7D \int \frac{du}{u})](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;%5Cfrac%7Bdu%7D%7Bu%7D)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;u&space;%5Cright&space;%7C&space;&plus;&space;C 	extup{ln}\left u ight + C)](http://www.codecogs.com/eqnedit.php?latex=%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;u&space;%5Cright&space;%7C&space;&plus;&space;C)

Question 4

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;e%5E%7Bu%7D%5C&space;du \int e^{u}\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;e%5E%7Bu%7D%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?e%5E%7Bu%7D&plus;C e^{u}+C)](http://www.codecogs.com/eqnedit.php?latex=e%5E%7Bu%7D&plus;C)

Question 5

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;a%5E%7Bu%7D%5C&space;du \int a^{u}\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;a%5E%7Bu%7D%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7Ba%5E%7Bu%7D%7D%7B%5Ctextup%7Bln%7Da%7D&space;&plus;&space;C \frac{a^{u}}{	extup{ln}a} + C)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7Ba%5E%7Bu%7D%7D%7B%5Ctextup%7Bln%7Da%7D&space;&plus;&space;C)

Question 6

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;sin%5C&space;u%5C&space;du \int sin\ u\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;sin%5C&space;u%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?-cos%5C&space;u&space;&plus;&space;C -cos\ u + C)](http://www.codecogs.com/eqnedit.php?latex=-cos%5C&space;u&space;&plus;&space;C)

Question 7

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;cos%5C&space;u \int cos\ u)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;cos%5C&space;u)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?sin%5C&space;u&space;&plus;&space;C sin\ u + C)](http://www.codecogs.com/eqnedit.php?latex=sin%5C&space;u&space;&plus;&space;C)

Question 8

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;sec%5E%7B2%7Du%5C&space;du \int sec^{2}u\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;sec%5E%7B2%7Du%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?tan%5C&space;u&space;&plus;&space;C tan\ u + C)](http://www.codecogs.com/eqnedit.php?latex=tan%5C&space;u&space;&plus;&space;C)

Question 9

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;csc%5E%7B2%7Du%5C&space;du \int csc^{2}u\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;csc%5E%7B2%7Du%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?-cot%5C&space;u&space;&plus;&space;C -cot\ u + C)](http://www.codecogs.com/eqnedit.php?latex=-cot%5C&space;u&space;&plus;&space;C)

Question 10

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;sec%5C&space;u%5C&space;%5C&space;tan%5C&space;u%5C&space;%5C&space;du \int sec\ u\ \ tan\ u\ \ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;sec%5C&space;u%5C&space;%5C&space;tan%5C&space;u%5C&space;%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?sec%5C&space;u&plus;C sec\ u+C)](http://www.codecogs.com/eqnedit.php?latex=sec%5C&space;u&plus;C)

Question 11

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;csc%5C&space;u%5C&space;cot%5C&space;u%5C&space;%5C&space;du \int csc\ u\ cot\ u\ \ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;csc%5C&space;u%5C&space;cot%5C&space;u%5C&space;%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?-csc%5C&space;u&space;&plus;&space;C -csc\ u + C)](http://www.codecogs.com/eqnedit.php?latex=-csc%5C&space;u&space;&plus;&space;C)

Question 12

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;tan%5C&space;u%5C&space;du \int tan\ u\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;tan%5C&space;u%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;sec%5C&space;u&space;%5Cright&space;%7C&space;&plus;&space;C 	extup{ln}\left sec\ u ight + C)](http://www.codecogs.com/eqnedit.php?latex=%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;sec%5C&space;u&space;%5Cright&space;%7C&space;&plus;&space;C)

Question 13

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;cot%5C&space;u%5C&space;du \int cot\ u\ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;cot%5C&space;u%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;sin%5C&space;u&space;%5Cright&space;%7C&plus;C 	extup{ln}\left sin\ u ight +C)](http://www.codecogs.com/eqnedit.php?latex=%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;sin%5C&space;u&space;%5Cright&space;%7C&plus;C)

Question 14

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;sec%5C&space;u%5C&space;%5C&space;du \int sec\ u\ \ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;sec%5C&space;u%5C&space;%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;%5C&space;sec%5C&space;u&plus;tan%5C&space;u%5C&space;%5Cright&space;%7C&plus;C 	extup{ln}\left \ sec\ u+tan\ u\ ight +C)](http://www.codecogs.com/eqnedit.php?latex=%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;%5C&space;sec%5C&space;u&plus;tan%5C&space;u%5C&space;%5Cright&space;%7C&plus;C)

Question 15

[![](http://latex.codecogs.com/gif.latex?%5Cint&space;csc%5C&space;u%5C&space;%5C&space;du \int csc\ u\ \ du)](http://www.codecogs.com/eqnedit.php?latex=%5Cint&space;csc%5C&space;u%5C&space;%5C&space;du)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;%5C&space;csc%5C&space;u-cot%5C&space;u%5C&space;%5Cright&space;%7C&plus;C 	extup{ln}\left \ csc\ u-cot\ u\ ight +C)](http://www.codecogs.com/eqnedit.php?latex=%5Ctextup%7Bln%7D%5Cleft&space;%7C&space;%5C&space;csc%5C&space;u-cot%5C&space;u%5C&space;%5Cright&space;%7C&plus;C)

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