Calculus
Basic Differentiation Rules
ddx[cu]=cu´ddx[cu]=cu´
ddx[u±v]=u´±v´ddx[u±v]=u´±v´
ddx[uv]=uv´+vu´ddx[uv]=uv´+vu´
ddx[uv]=vu´+uv´v2ddx[uv]=vu´+uv´v2
ddx[c]=0ddx[c]=0
ddx[un]=nun-1u´ddx[un]=nun−1u´
ddx[x]=1ddx[x]=1
ddx[|u|]=u|u|(u´), u≠0ddx[|u|]=u|u|(u´), u≠0
ddx[lnu]=u´uddx[lnu]=u´u
ddx[eu]=euu´ddx[eu]=euu´
ddx[logau]=u´(lna)uddx[logau]=u´(lna)u
ddx[au]=(lna)auu´ddx[au]=(lna)auu´
ddx[sinu]=(cosu)u´ddx[sinu]=(cosu)u´
ddx[cosu]=-(sinu)u´ddx[cosu]=−(sinu)u´
ddx[tan u]=(sec2 u)u´ddx[tan u]=(sec2 u)u´
ddx[cot u]=-(csc2 u)u´ddx[cot u]=−(csc2 u)u´
ddx[sec u]=(sec u tan u)u´ddx[sec u]=(sec u tan u)u´
ddx[csc u]=-(csc u cot u)u´ddx[csc u]=−(csc u cot u)u´
ddx[arcsin u]=u´√1-u2ddx[arcsin u]=u´√1−u2
ddx[arc cos u]=-u´√1-u2ddx[arc cos u]=−u´√1−u2
ddx[arc tan u]=u´1+u2ddx[arc tan u]=u´1+u2
ddx[arc cot u]=-u´1+u2ddx[arc cot u]=−u´1+u2
ddx[arc sec u]=u´|u|√u2-1ddx[arc sec u]=u´|u|√u2−1
ddx[arc csc u]=-u´|u|√u2-1ddx[arc csc u]=−u´|u|√u2−1
Basic Integration Rules (a > 0)
∫k f(u)du=k∫f(u)du
∫[f(u)±g(u)]du=∫f(u)du ±∫g(u)du
∫du=u+C
∫undu=un+1n+1+C, n≠-1
∫duu=ln|u|+C
∫eudu=eu+C
∫audu=(1lna)au+C
∫sinu du=-cosu+C
∫cosu du=sinu+C
∫tanu du=-ln|cosu|+C
∫cotu du=ln|sinu|+C
∫secu du=ln|secu+tanu|+C
∫cscu du=-ln|cscu +cotu| + C
∫secu du =ln|secu+tanu|+C
∫cscu du =-ln|cscu+cotu|+C
∫sec2u du =tanu+C
∫csc2u du =-cotu+C
∫secu tan u du =secu+C
∫csc u cot u du =-csc u+C
∫du2√a2-u2= arcsin ua+ C
∫dua2+u2= 1aarctan ua+ C
∫duu2√u2-a2= 1aarcsec |u|a+ C