Integrals
5sinh(7x-2)dx
5/7 cosh(7x+2)+C
2x^3
6x^2
dy/dx=2xy
ln|y|=x^2+C
Solve for fractions with new numerators.
(3x+5)
--------
(x+1)(x-2)
-2/3 + 11/3
------- ---------
x+1 x-2
4ln(x)/x^6 dx
(-5ln(x)-1)/25 +C
sin(4x)
4cos(4x)
dy/dx=(x^2-2)(2y+3)
ln|2y+3|=2/3 x^3-4x+C
Solve for fractions with new numerators.
x
---------
(x-1)^2
1 + 1
----- ----------
x-1 (x-1)^2
tan(x)sec^3(x)dx
1/4 sec^4(x) +C
log_3(2x+4)
2/(ln3(2x+4))
dy/dx=3y^4(x^1/2)
-1/3 y^-3=2x^3/2 +C
2x+3
------------------
(x^2+1)(x-2)
-7/5 x - 4/5 + 7/5
--------------- ---------
x^2+1 x-2
5sin^-1(x)dx
5xsin^1(x)-10(1-x^2)^1/2 +C
x^4tanh(3x)
4x^3tanh(3x)+3x^4sech^2(3x)
dy/dx=9+3x+3y+xy
ln|y+3|=1/2 x^2 +3x+C
3x^2+x+2
--------------
(x-1)^2(x+2)
5/3 + 2 + 4/3
----- ------ --------
x-1 (x-1)^2 x+2
Integral from 2 to infinity of 9/(1-3x)^4
1/125
ln(cosh(2x))
2tanh(2x)
dy/dx=(3x+1)(y^2+4)=3xy^2+12x+y^2+4
(In terms of theta and x
1/8 theta+1/4 sin(2theta)=3/2 x^2 + x +C
x^3+2x^2+x+4
-------------------
(x^2+1)(x-1)^2
x + 4
------- ---------
x^2+1 (x-1)^2