Trigonometric Integral Table

Trig Integral Table can be categorized as Trigonometric Integral Table; Inverse Trigonometric Integral table and Hyperbolic Integral table

Trigonometric Integral Table consists of the following functions:
Integral [sin (x)]dx = - cos(x) +c
The General Rule is given by, Integral[sin(ax+b)]dx = -1/a[cos(ax+b)]  + c
Integral[sin^2(ax)]dx = (x/2) –[sin(2ax)]/4a
Integral[sin^3(ax)]dx= [-3cos(ax)/4a] + [cos(3ax)/12a]

Integral[cos(x)] dx= sin(x) +c
The General Rule is given by, Integral [cos(ax+b)]dx = 1/a[sin(ax+b)] + c
Integral[cos^2(ax)]dx = (x/2) + [sin(2ax)]/4a
Integral[cos^3(ax)]dx= [3sin(ax)]/4a + [sin(3ax)]/12a

Integral[cos(x)sin(x)]dx=(1/2)sin^2(x) + c1= (-1/2)cos^2(x) +c2 = (-1/4)[cos(2x)] + c3
Integral[cos(ax)sin(bx)]dx = cos[(a-b)x]/2(a-b) – cos[(a+b)x]/2(a+b), a is not equal to b

Integral[sin^2(x)cos(x)]dx = (1/3)sin^3(x)
Integral[cos^2(ax)sin(ax)]dx = (-1/3a)cos^3(ax)
Integral[sin^2(ax)cos^2(ax)]dx = (x/4) – [sin(2ax)]/8a – sin[2(a-b)x]/16(a-b) + sin(2bx)/8b – sin[2(a+b)x]/16(a+b)

Integral[tan(x) dx= - ln|cos(x)| + c
The General Rule is given by, Integral[tan(ax+b)]dx = -1/a[ln|cos(ax+b)| + c
Integral[tan(ax)]dx = (-1/a)ln(cos ax)
Integral[tan^2(ax)]dx = -x + (1/a) tan(ax)
Integral[tan^3(ax)]dx = (1/a)ln[cos(ax)] + (1/2a)sec^2(ax)

Integral[csc(x)]dx= -ln|csc(x) + cot(x)| +c
The General Rule is given by, Integral[csc(ax+b)]dx= -1/a[ln|csc(ax+b) + cot(ax+b)| + c

Integral[sec(x)]dx = ln|sec(x)+ tan(x)|+c = 2 tanh^-1[tan(x/2)]
The General Rule is given by, Integral[sec(ax+b)]dx = 1/a[ln|sec(ax+b) +tan(ax+b)| + c
Integral[sec^2(x)]dx = tan(x) + c
Integral[sec^2(ax)]dx = (1/a)tan(ax)
Integral[sec^3(ax)]dx = (1/2) sec(x)tan(x) + (1/2)ln |sec(x) + tan(x)|
Integral[sec(x)tan(x)]dx= sec(x)
Integral[sec^2(x)tan(x)]dx = (1/n)sec^n(x), n is not equal to zero

Integral[cot(x)]dx = ln|sin(x)| +c
The General Rule is given by, Integral[cot(ax+b)]dx = 1/a[ln|sin(ax+b)| + c

Integral[csc^2(x)] dx = - cot(x) + c
Integral[csc^2(ax)]dx =(-1/a)cot(ax)
Integral[csc^3(x)dx] = (-1/2)cot(x)csc(x) + (1/2)ln|csc(x) – cot(x)|
Integral[csc(x)cot(x)]dx = -csc(x) + c
Integral[csc^n(x)cot(x)]dx= (-1/n) csn^n(x), n is not equal to zero

Table of Integrals of Inverse Trigonometric functions
Integral [arc sin(x)] dx = x arc sin(x) + sqrt(1- x^2) + c
Integral[arc cos(x)] dx = x arc cos(x) – sqrt(1-x^2) + c
Integral[arc tan(x)] dx = x arc tan(x) – ½[ln(1+x^2)] + c
Integral [ dx/sqrt(1-x^2)] = arc sin(x) + c
Integral[dx/ x[sqrt(x^2-1)] = arc sec|x|+ c

Table of Integral of Hyperbolic Functions
Integral[sinh(x) dx] = cosh(x) +c
Integral[cosh(x) dx]= sinh (x) +c
Integral[tanh(x) dx]= ln[cosh (x)]+ c
Integral[csch(x) dx]= ln|tanh(x/2)| + c
Integral[sech(x)dx]= arc tan[sinh(x)] + c
Integral[coth(x)dx]= ln|sinh(x)| + c
Integral[cos(ax)cosh(bx)]dx = [1/(a^2+b^2)][asin(ax)cosh(bx)+bcos(ax)sinh(bx)]
Integral[cos(ax)sinh(bx)]dx = [1/(a^2+b^2)][bcos(ax)cosh(bx)+a sin(ax)sinh(bx)]
Integral[sin(ax)cosh(bx)]dx = [1/(a^2+b^2)][-acos(ax)cosh(bx)+bsin(ax)sinh(bx)]
Integral[sin(ax)sinh(bx)]dx = [1/(a^2+b^2)][bcosh(bx)sin(ax)- acos(ax)sinh(bx)]
Integral[sinh(ax)cosh(ax)]dx = (1/4a)[-2ax + sinh(2ax)]
Integral[sinh(ax)cosh(bx)]dx= (1/b^2-a^2)[bcosh(bx)sinh(ax) – a cosh(ax)sinh(bx)]