Exponentially Cooked
Evaluate the integral
1/x dx from -3 to -2
ln(2/3)
Evaluate the differential eqution
dy/dx = ex-y
What is
y=ln(ex+C)
Evaluate the integral
sin3x dx
What is cos3x/3 - cosx +C
Expand the quotients by partial fractions
(5x-13) / ((x-3)(x-2))
What is
2/(x-3) + 3/(x-2)
Evaluate the integral
1 / sqrt(1 - x2) from 0 to 1
What is π/2
Evaluate the integral
esqrt(r) / sqrt(r) dr
What is 2esqrt(r)+C?
Solve the differential equation
sqrt(2xy) dy/dx = 1
What is
y = (3/2(sqrt(2)x3/2+C))2/3
Evaluate the integral
sin3x cos3x dx
What is
cos6x / 6 + cos4x / 4 + C
Evaluate the integral
4x cos(2-3x)
What is
(-4x/3) sin(2-3x) + (4/9)cos(2-3x) + C
Evaluate the integral
x lnx from 0 to 1
What is -(1/4)
Evaluate the integral
x2x^2 from 1 to sqrt 2
What is 1/ln2?
Solve the differential equation
y2 dy/dx = 3x2y3 - 6x2
What is
y= (Ae3x^3+2)1/3
sec2x tanx
What is
tan2x / 2 +C
Express the integrand as sum of partial fractions and evaluate the integrals
(x+4) / (x2+5x+6)
(2/7) ln| x + 6 | + (5/7) ln|x- 1| + C
Evaluate the integral
θeθ from -∞ to 0
What is -1
Evaluate the integral
log2x / x from 1 to 4
What is 2(ln4)^2 / ln(2)
Solve the differential equation
sec(x) dy/dx = ey + sinx
What is
y = -ln(-esinx-C)
Evaluate the integral
sqrt( 1 - cos2x) from 0 to π
What is
2 sqrt(2)
Evaluate the integral
eθcosθ
What is
(1/2) ( eθcosθ + eθsinθ) + C
Evaluate the integral
(s+1) / sqrt(4 - s2)
What is π / 2 + 2
Evaluate the integral
e(-1/x^2) / x3
What is -(1/2)e-(1/x^2)+C
Solve the differential equation
dy/dx = ex-y + ex + e-y + 1
What is
y = ln(Aee^x + x -1)
sqrt(1 - 9t2)
What is
(1/2)sqrt(1-9t2) + (1/6)sin-1(3t) +C
Express the integrand as a sum of partial fractions and evaluate the integrals
(y2+2y+1)/(y2+1)2
What is
arctan(y) - 1/(y2+1) + C