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Power of x.| xn dx = xn+1 (n+1)-1 + C (n -1) Proof | x-1 dx = ln|x| + C |
| ex dx = ex + C Proof | bx dx = bx / ln(b) + C Proof, Tip! |
| ln(x) dx = x ln(x) - x + C Proof |
| sin x dx = -cos x + C Proof | csc x dx = - ln|csc x + cot x| + C Proof |
| cos x dx = sin x + C Proof | sec x dx = ln|sec x + tan x| + C Proof |
| tan x dx = -ln|cos x| + C Proof | cot x dx = ln|sin x| + C Proof |
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Trigonometric Result| cos x dx = sin x + C Proof | csc x cot x dx = - csc x + C Proof |
| sin x dx = -cos x + C Proof | sec x tan x dx = sec x + C Proof |
| sec2 x dx = tan x + C Proof | csc2 x dx = - cot x + C Proof |
| arcsin x dx = x arcsin x + (1-x2) + C |
| arccsc x dx = x arccos x - (1-x2) + C |
| arctan x dx = x arctan x - (1/2) ln(1+x2) + C |
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| sinh x dx = cosh x + C Proof | csch x dx = ln |tanh(x/2)| + C Proof |
| cosh x dx = sinh x + C Proof | sech x dx = arctan (sinh x) + C |
| tanh x dx = ln (cosh x) + C Proof | coth x dx = ln |sinh x| + C Proof |
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| To solve a more complicated integral, see The Integrator at http://integrals.com. |