The integrals below involve `cos ax`.
1) `int cos ax dx = (sin ax)/a`
2) `int x cos ax dx = (cos ax)/a^2+(x sin ax)/a`
3) `int x^2 cos ax dx = (2x)/a^2cos ax+(x^2/a-2/a^3)sin ax`
4) `int x^3 cos ax dx = ((3x^2)/a^2-6/a^4)cos ax+(x^3/a-(6x)/a^3)sin ax`
5) `int (cos ax)/x dx = ln x-(ax)^2/(2*2!)+(ax)^4/(4*4!)-(ax)^6/(6*6!)+...`
6) `int (cos ax)/x^2 dx = -(cos ax)/x-aint (sin ax)/x dx`
**[See integral #5 in the previous table; forms involving `sin ax`]
7) `int 1/(cos ax) dx = 1/a ln (secax+tan ax)=1/aln tan(pi/4+(ax)/2)`
8) `int x/(cos ax) dx = 1/a^2{(ax)^2/2+(ax)^4/8+(5(ax)^6)/144+...+(E_n(ax)^(2n+2))/((2n+2)(2n )!)+...}`
9) `int cos^2 ax dx = x/2+(sin 2ax)/(4a)`
10) `int x*cos^2ax dx = x^2/4+(x*sin 2ax)/(4a)+(cos 2ax)/(8a^2)`
11) `int cos^3 ax dx = (sin ax)/a-(sin^3ax)/(3a)`
12) `int cos^4 ax dx = (3x)/8+(sin 2ax)/(4a)+(sin 4ax)/(32 a)`
13) `int 1/(cos^2 ax) dx = (tan ax)/a`
14) `int 1/(cos^3 ax) dx = (sin ax)/(2a*cos^2 ax)+1/(2a) ln tan(pi/4+(ax)/2)`
15) `int cos ax*cos px dx = (sin(a-p)x)/(2(a-p))+(sin(a+p)x)/(2(a+p)`
**[If `a=+-p`, see integral #9 in this table]
16) `int 1/(1-cos ax) dx = -1/acot((ax)/2)`
17) `int x/(1-cos ax) dx = -x/acot((ax)/2)+2/a^2 ln sin((ax)/2)`
18) `int 1/(1+cos ax) dx = 1/a tan((ax)/2)`
19) `int x/(1+cos ax) dx = x/a tan((ax)/2)+2/a^2 ln cos((ax)/2)`
20) `int 1/(1-cos ax)^2 dx = -1/(2a)cot((ax)/2)-1/(6a)cot^3((ax)/2)`
21) `int 1/(1+cos ax)^2 dx = 1/(2a)tan((ax)/2)+1/(6a)tan^3((ax)/2)`
22) `int 1/(p+q cos ax) dx = 2/(asqrt(p^2-q^2)) tan^-1sqrt((p-q)/(p+q))tan(1/2ax)`
OR `= 1/(asqrt(q^2-p^2))ln((tan(1/2ax)+sqrt((q+p)/(q-p)))/(tan(1/2ax)-sqrt((q+p)/(q-p))))`
**[If `p=+-q`, see integrals #16 and #18 in this table]
23) `int 1/(p+q cos ax)^2 dx = (q sin ax)/(a(q^2-p^2)(p+q cos ax))-p/(q^2-p^2)int 1/(p+q cos ax) dx`
**[If `p=+-q`, see integrals #20 and #21 in this table]
24) `int 1/(p^2+q^2 cos^2 ax) dx = 1/(apsqrt(p^2+q^2))tan^-1((p tan ax)/sqrt(p^2+q^2))`
25) `int 1/(p^2-q^2 cos^2 ax) dx = 1/(apsqrt(p^2-q^2))tan^-1((p tan ax)/sqrt(p^2-q^2))`
OR `= 1/(2apsqrt(q^2-p^2))ln((p tan ax-sqrt(q^2-p^2))/(p tan ax+sqrt(q^2-p^2)))`
26) `int x^m cos ax dx = (x^m sin ax)/a+(mx^(m-1))/a^2 cos ax-(m(m-1))/a^2int x^(m-2) cos ax dx`
27) `int (cos ax)/x^n dx = -(cos ax)/((n-1)x^(n-1))-a/(n-1)int (sin ax)/x^(n-1) dx`
**[See integral #27 in the previous table; forms involving `sin ax`]
28) `int cos^n ax dx = (sin ax*cos^(n-1) ax)/(an)+(n-1)/nint cos^(n-2) ax dx`
29) `int 1/(cos^n ax) dx = (sin ax)/(a(n-1)cos^(n-1) ax)+(n-2)/(n-1)int 1/(cos^(n-2) ax) dx`
30) `int x/(cos^n ax) dx = (x sin ax)/(a(n-1)cos^(n-1) ax)-1/(a^2(n-1)(n-2)cos^(n-2) ax)+(n-2)/(n-1)int x/(cos^(n-2) ax) dx`