Integration by Standard Form

∫ ( x + ) dx
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Summary
∫ (ax + b)n dx =1 (ax + b)n+1+ c       if n ≠ -1
a n + 1
∫     1     dx =1ln | ax + b |+ c
ax + ba
∫ eax+b dx =eax+b+ c
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a
∫ sin (ax+b) dx =-cos (ax+b)+ c
a
∫ cos (ax+b) dx =sin (ax+b)+ c
a
∫ tan x dx= ln | sec 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
∫ sin2 x dx =1∫ 1 - cos 2x dx
2
∫ cos2 x dx =1∫ 1 + cos 2x dx
2
∫ sec2 x dx= tan x + c
∫ cosec2 x dx= -cot x + c
∫ tan2 x dx= ∫ sec2 x - 1 dx
∫ cot2 x dx= ∫ cosec2 x - 1 dx
∫ ax dx =ax+ c
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ln a
∫      1      dx =sin-1x+ c
√(a2 - x2)a
∫     1     dx =1tan-1x+ c
a2 + x2aa