Common Intergrals

Question 1

∫ xⁿ dx

Answer 1

xⁿ⁺¹/n+1 + c

Question 1

∫ 1/x dx

Answer 1

ln|x| + c

Question 2

∫ sin(x) dx

Answer 2

-cos(x) + c

Question 3

∫ cos(x) dx

Answer 3

sin(x) + c

Question 4

∫ eˣ dx

Answer 4

eˣ + c

Question 5

∫ tan(x) dx

Answer 5

-In|cos(x)| + c

Question 6

∫ cos(πx) dx

Answer 6

sin(πx)/π + c

Question 7

∫ cot(x) dx

Answer 7

In|sin(x)| + c

Question 8

∫ sec(x) dx

Answer 8

In|sec(x) + tan(x)| + c

Question 9

∫ csc(x) dx

Answer 9

In|csc(x) - cot(x)| + c

Question 10

∫ ln(x) dx

Answer 10

xlnx - x + c

Question 11

∫ sin(x)cos(x) dx

Answer 11

sin²(x)/2 + c

-cos²(x)/2 + c

Question 12

∫ sin(x)tan(x) dx

Answer 12

In|sec(x) + tan(x)|- sin(x) + c

Question 14

Integration By Parts

Answer 14

∫ u(dv) = uv - ∫ v(du)