Derivatives-Integrals-Trig-Formula-Sheet

Integral of e^u

The integral of e^u with respect to u is e^u + C.

Derivative of sin(u)

The derivative of sin(u) is cos(u)u'.

Derivative of cos(u)

The derivative of cos(u) is -sin(u)u'.

Integration of sec^2(u)

The integral of sec^2(u) with respect to u is tan(u) + C.

Derivation of arcsin(u)

The derivative of arcsin(u) is u'/sqrt(1-u^2).

Logarithmic Derivative (loga(u))

The derivative of log_a(u) is u’/(u ln(a)).

Integration of csc^2(u)

The integral of csc^2(u) with respect to u is -cot(u) + C.

Basic Integration Formula

J f(u) du = F(u) + C, where F is the antiderivative of f.

Integration of tan(u)

The integral of tan(u) with respect to u is -ln|cos(u)| + C.

Derivative of arctan(u)

The derivative of arctan(u) is u'/(1+u^2).

Integration of cos(u)

The integral of cos(u) with respect to u is sin(u) + C.

Integration of sin(u)

The integral of sin(u) with respect to u is -cos(u) + C.

Integration of csc(u)

-ln|csc(u) + cot(u)| + C. |

integration of sec(u)

The integral of sec(u) with respect to u is ln|sec(u) + tan(u)| + C.

derivative of tan(u)

The derivative of tan(u) with respect to u is sec²(u).