Formula sheet

Question 1

What is the integral of ( u^n ) with respect to ( u )?

Answer 1

( int u^n du = rac{u^{n+1}}{n+1} + C ) (for ( n
eq -1 ))

Question 2

What is the integral of ( rac{1}{u} ) with respect to ( u )?

Answer 2

( int rac{1}{u} du = ln |u| + C )

Question 3

What is the integral of ( a^u )?

Answer 3

( int a^u du = rac{a^u}{ln a} + C ) (for ( a > 0, a
eq 1 ))

Question 4

What is the integral of ( sin u )?

Answer 4

( int sin u du = -cos u + C )

Question 5

What is the integral of ( cos u )?

Answer 5

( int cos u du = sin u + C )

Question 6

What is the integral of ( sec^2 u )?

Answer 6

( int sec^2 u du = an u + C )

Question 7

What is the integral of ( csc^2 u )?

Answer 7

( int csc^2 u du = -cot u + C )

Question 8

What is the integral of ( rac{1}{u^2 + a^2} )?

Answer 8

( int rac{1}{u^2 + a^2} du = rac{1}{a} arctan rac{u}{a} + C )

Question 9

What is the integral of ( rac{1}{u^2 - a^2} )?

Answer 9

( int rac{1}{u^2 - a^2} du = rac{1}{2a} ln left| rac{u - a}{u + a}
ight| + C )

Question 10

What is the integral of ( rac{1}{sqrt{u^2 + a^2}} )?

Answer 10

( int rac{1}{sqrt{u^2 + a^2}} du = ln left| u + sqrt{u^2 + a^2}
ight| + C )

Question 11

What is the integral of ( rac{1}{sqrt{a^2 - u^2}} )?

Answer 11

( int rac{1}{sqrt{a^2 - u^2}} du = arcsin rac{u}{a} + C )