(3x + 4)2 | (3x + 4)-2 | (3x + 4)-1 | (3x + 4)1/2 |
(3x + 4)-1/2 | (3x + 4)3/2 | ex+3 | e2x |
sin (2x) | cos (2x) | tan (2x) | sec2 (3x + 4) |
1 / sqrt(4 - x2) | 1 / sqrt(1 - 9x2) | 1 / sqrt(4 - 9x2) | |
1 / (4 + x2) | 1 / (1 + 9x2) | 1 / (4 + 9x2) |
∫ (ax + b)n dx = | 1 | (ax + b)n+1 | + c if n not = -1 |
_ | _________ | ||
a | n + 1 |
∫ | 1 | dx = | 1 | ln | ax + b | | + c |
ax + b | a |
∫ eax+b dx = | eax+b | + c |
_____ | ||
a |
∫ sin (ax+b) dx = | - cos (ax+b) | + c | ∫ cos (ax+b) dx = | sin (ax+b) | + c | |
a | a |
∫ sin2 x dx = | 1 | ∫ 1 - cos 2x dx | ∫ cos2 x dx = | 1 | ∫ 1 + cos 2x dx | |
2 | 2 |
∫ sec2 (ax+b) dx = | tan (ax+b) | + c | ∫ cosec2 (ax+b) dx = | - cot (ax+b) | + c | |
a | a |
∫ tan2 x dx = ∫ sec2 x - 1 dx | ∫ cot2 x dx = ∫ cosec2 x - 1 dx | |
∫ tan x dx = - ln | cos x | + c | ∫ cot x dx = ln | sin x | + c | |
∫ sec x dx = ln | sec x + tan x | + c | ∫ cosec x dx = - ln | cosec x + cot x | + c |
∫ ax dx = | ax | + c |
___ | ||
ln a |
∫ | 1 | dx = | sin-1 | x | + c | ∫ | 1 | dx = | 1 | tan-1 | x | + c | |
sqrt ( a2 - x2 ) | a | a2 + x2 | a | a |