Calc BC Unit 2 formula review

Derivative of sinx

cosx

Derivative of tanx

sec²x

Derivative of secx

secx tanx

Derivative of cosx

-sinx

Derivative of cotx

-csc²x

Derivative of cscx

-cscx cotx

derivative of arcsin

\frac{1}{\sqrt{1-x^2}}

derivative of arccos

-\frac{1}{\sqrt{1-x^2}}

derivative of arctan

\frac{1}{1+x^2}

\int^{}\sin u\,dx

-\cos u+c

\int^{}\cos u\,dx

sinu + c

\int^{}\tan u\,dx

-\ln\left\vert\cos u\right\vert+c

\int^{}\cot u\,dx

\ln\left\vert\sin u\right\vert+c

\int^{}\sec u\,dx

\ln\left\vert\sec u+\tan u\right\vert+c

\int^{}\csc u\,dx

-\ln\left\vert\csc u+\cot u\right\vert+c

\int^{}\sec^2u\,dx

\tan u+c

\int^{}\csc^2u\,dx

-cotu+c

\int^{}\sec u\tan u\,dx

secu+c

\int^{}\csc u\cot u\,dx

-cscu+c

\frac{du}{\sqrt{a^2-u^2}}

\arcsin\frac{u}{a}

\frac{du}{a^2+u^2}

\frac{1}{a}\arcsin\frac{u}{a}

\frac{du}{\sqrt{a^2-u^2}}

\frac{1}{a}\frac{\operatorname{arcsec}u}{a}

sin²x+cos²x =

1

sin²x =

\frac{1-\cos2x}{2}

cos²x =

\frac{1+\cos2x}{2}

if sine is odd and positive

keep one sine and convert rest to cosines

if cosine is odd and positive

keep one cosine and convert rest to sines

sinmxsinnx

½ (cos[(m-n)x]-cos[(m+n)x])

sinmxcosnx

½ (sin[(m-n)x]+sin[(m+n)x])

cosmxcosnx

½ (cos[(m-n)x]+cos[(m+n)x])

\sqrt{a^2+x^2}

a\sin\theta

\sqrt{a^2+x^2}

a\tan\theta

\sqrt{x^2-a^2}

a\sec\theta

1-sin² \theta

cos^ \theta

1+tan² \theta  

sec² \theta  

sec² \theta -1

tan² \theta

\int_1^{\infty}\!\frac{dx}{x^{p}}\,p>1

\frac{1}{p-1}

\int_1^{\infty}\!\frac{dx}{x^{p}}\,p<1

diverges