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Popular Calculus Problems

integral from-0.5 to 0.5 of 1.5x^2	\int\:_{-0.5}^{0.5}1.5x^{2}dx
derivative of y=(3x-2)^2(5x+4)	derivative\:y=(3x-2)^{2}(5x+4)
inverse oflaplace (-1)/(s^2-1)	inverselaplace\:\frac{-1}{s^{2}-1}
derivative of 2/x+sqrt(x)	\frac{d}{dx}(\frac{2}{x}+\sqrt{x})
(\partial)/(\partial v)(1/(u^2+v^2))	\frac{\partial\:}{\partial\:v}(\frac{1}{u^{2}+v^{2}})
integral of (7+6x)/(1+x^2)	\int\:\frac{7+6x}{1+x^{2}}dx
limit as x approaches 3 of 2x-5	\lim\:_{x\to\:3}(2x-5)
limit as x approaches pi/x of xcos(x)	\lim\:_{x\to\:\frac{π}{x}}(x\cos(x))
limit as x approaches-2 of \sqrt[3]{x+2}	\lim\:_{x\to\:-2}(\sqrt[3]{x+2})
tangent of y=(5x)/(x+2)(3.3)	tangent\:y=\frac{5x}{x+2}(3.3)
(dy)/(dx)=-(x+6)/(7y^2)	\frac{dy}{dx}=-\frac{x+6}{7y^{2}}
limit as x approaches-pi/3 of sec(x)	\lim\:_{x\to\:-\frac{π}{3}}(\sec(x))
(\partial)/(\partial x)(-arctan(y/x))	\frac{\partial\:}{\partial\:x}(-\arctan(\frac{y}{x}))
4x^2+5y(dy)/(dx)=0	4x^{2}+5y\frac{dy}{dx}=0
x^{''}+x^'-2x=e^t	x^{\prime\:\prime\:}+x^{\prime\:}-2x=e^{t}
integral from 0 to 4 of pix^2	\int\:_{0}^{4}πx^{2}dx
derivative of-5e^{-x/3}+2	derivative\:-5e^{-\frac{x}{3}}+2
limit as x approaches-4 of (x-4)/(x-8)	\lim\:_{x\to\:-4}(\frac{x-4}{x-8})
limit as x approaches infinity of arcsin((2x)/(5+4x))	\lim\:_{x\to\:\infty\:}(\arcsin(\frac{2x}{5+4x}))
(\partial)/(\partial x)(e^{4xy}*4y)	\frac{\partial\:}{\partial\:x}(e^{4xy}\cdot\:4y)
x^2y^'+2xy=5y^3	x^{2}y^{\prime\:}+2xy=5y^{3}
(x^2+1)(dy)/(dx)+6x(y-1)=0	(x^{2}+1)\frac{dy}{dx}+6x(y-1)=0
y^'=((x^2+y))/(x+1)	y^{\prime\:}=\frac{(x^{2}+y)}{x+1}
y^'+y/x =x^{-4}	y^{\prime\:}+\frac{y}{x}=x^{-4}
derivative of s(t)=14+15sin(14pit)	derivative\:s(t)=14+15\sin(14πt)
(x^2-2xy)dx+xdy=0	(x^{2}-2xy)dx+xdy=0
laplacetransform sin^2(pit)	laplacetransform\:\sin^{2}(πt)
integral of sin(pi/2)	\int\:\sin(\frac{π}{2})dx
integral of cot^5(x)*csc^3(x)	\int\:\cot^{5}(x)\cdot\:\csc^{3}(x)dx
8(d^2y)/(dx^2)+3(dy)/(dx)+9y=0	8\frac{d^{2}y}{dx^{2}}+3\frac{dy}{dx}+9y=0
sum from n=0 to infinity of ln(1+1/n)	\sum\:_{n=0}^{\infty\:}\ln(1+\frac{1}{n})
y^{''}-10y^'+34y=0,y(0)=2,y^'(0)=3	y^{\prime\:\prime\:}-10y^{\prime\:}+34y=0,y(0)=2,y^{\prime\:}(0)=3
slope ofintercept (-3,-1),(-2,-2)	slopeintercept\:(-3,-1),(-2,-2)
integral of 1/(\sqrt[5]{x)}	\int\:\frac{1}{\sqrt[5]{x}}dx
integral of ((sqrt(x)+1)^2)/(2sqrt(x))	\int\:\frac{(\sqrt{x}+1)^{2}}{2\sqrt{x}}dx
3y^{''}+13y^'+4y=0,y(0)=-2,y^'(0)=-2	3y^{\prime\:\prime\:}+13y^{\prime\:}+4y=0,y(0)=-2,y^{\prime\:}(0)=-2
integral of (5x^3-3x^2+7)	\int\:(5x^{3}-3x^{2}+7)dx
derivative of x^4-8x^2+16	\frac{d}{dx}(x^{4}-8x^{2}+16)
d/(dy)(1/(y^3))	\frac{d}{dy}(\frac{1}{y^{3}})
(\partial)/(\partial x)(2x^2+5y^2-xy)	\frac{\partial\:}{\partial\:x}(2x^{2}+5y^{2}-xy)
integral from x to x^2 of e^{t^2}	\int\:_{x}^{x^{2}}e^{t^{2}}dt
derivative of y=(5(1-sin(x)))/(2cos(x))	derivative\:y=\frac{5(1-\sin(x))}{2\cos(x)}
derivative of tan^4(x^3)	derivative\:\tan^{4}(x^{3})
area f(x)=x^2,x=5	area\:f(x)=x^{2},x=5
f(x)=(sin(x))/(1+2cos(x))	f(x)=\frac{\sin(x)}{1+2\cos(x)}
y^'=y-2	y^{\prime\:}=y-2
(\partial)/(\partial x)(xln(z^7+x^3))	\frac{\partial\:}{\partial\:x}(x\ln(z^{7}+x^{3}))
derivative of y= 1/(2sqrt(x-2))	derivative\:y=\frac{1}{2\sqrt{x-2}}
limit as x approaches 7 of (2x+1)/(x-7)	\lim\:_{x\to\:7}(\frac{2x+1}{x-7})
integral of 2cos(5x)	\int\:2\cos(5x)dx
(dy)/(dx)=y(4x^2+1)	\frac{dy}{dx}=y(4x^{2}+1)
derivative of y= x/3	derivative\:y=\frac{x}{3}
derivative of 8pi^7	derivative\:8π^{7}
d/(dy)((x+y)^2)	\frac{d}{dy}((x+y)^{2})
derivative of sqrt(x)*(x-14)	derivative\:\sqrt{x}\cdot\:(x-14)
(\partial)/(\partial t)(tsin(t))	\frac{\partial\:}{\partial\:t}(t\sin(t))
derivative of arcsin(x+1)	\frac{d}{dx}(\arcsin(x+1))
integral from 2 to x^2 of cos(x^2+1)	\int\:_{2}^{x^{2}}\cos(x^{2}+1)dx
integral from 0 to 2pi of x^2sin(2x)	\int\:_{0}^{2π}x^{2}\sin(2x)dx
d/(dt)(3sin(3t))	\frac{d}{dt}(3\sin(3t))
((2y)/x+2x)+(2ln(x)-3)y^'=0	(\frac{2y}{x}+2x)+(2\ln(x)-3)y^{\prime\:}=0
(\partial)/(\partial x)((26x^2)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{26x^{2}}{(x-y)^{2}})
tangent of 1+4x^2-2x^3	tangent\:1+4x^{2}-2x^{3}
derivative of sqrt(sin(x-1(x^3)))	\frac{d}{dx}(\sqrt{\sin(x-1)(x^{3})})
derivative of x-4	derivative\:x-4
integral of xcos(9x)	\int\:x\cos(9x)dx
limit as x approaches 6 of 9	\lim\:_{x\to\:6}(9)
(dy)/(dt)+t^2y=1	\frac{dy}{dt}+t^{2}y=1
(\partial)/(\partial x)(e^xcos(y))	\frac{\partial\:}{\partial\:x}(e^{x}\cos(y))
y^'-2/(x^2)y=0	y^{\prime\:}-\frac{2}{x^{2}}y=0
f(x)=2x^2ln(2x)	f(x)=2x^{2}\ln(2x)
((1-x)/y)dx=-x^2cos(y)dy	(\frac{1-x}{y})dx=-x^{2}\cos(y)dy
(\partial)/(\partial x)(sqrt(4-x^2-y))	\frac{\partial\:}{\partial\:x}(\sqrt{4-x^{2}-y})
derivative of 2/(sqrt(4x-17))	derivative\:\frac{2}{\sqrt{4x-17}}
derivative of cos(x-2xy)	\frac{d}{dx}(\cos(x)-2xy)
y^'+4y=cos(4t),y(0)=2	y^{\prime\:}+4y=\cos(4t),y(0)=2
simplify 1/3 x^{3/2}-x^{1/2}	simplify\:\frac{1}{3}x^{\frac{3}{2}}-x^{\frac{1}{2}}
integral of 1/(x^3)	\int\:\frac{1}{x^{3}}dx
f(x)=x^{1/5}	f(x)=x^{\frac{1}{5}}
(\partial)/(\partial x)(sin(5x-3y))	\frac{\partial\:}{\partial\:x}(\sin(5x-3y))
limit as x approaches 2 of 5x-14x^{-2}	\lim\:_{x\to\:2}(5x-14x^{-2})
integral from 0 to pi of (1-sin(x))	\int\:_{0}^{π}(1-\sin(x))dx
limit as x approaches 13 of sqrt(x-4)	\lim\:_{x\to\:13}(\sqrt{x-4})
derivative of 4x^3-2x+5	derivative\:4x^{3}-2x+5
integral of (x^4-6x^2-2x+4)	\int\:(x^{4}-6x^{2}-2x+4)dx
0^'	0^{\prime\:}
(dy)/(dx)=(2x)/(e^{2y)}	\frac{dy}{dx}=\frac{2x}{e^{2y}}
area x^2,2x	area\:x^{2},2x
f(x)=ln(ln(5x))	f(x)=\ln(\ln(5x))
integral of e^{-t^8}	\int\:e^{-t^{8}}dt
derivative of (4x^2-13^{-14})	\frac{d}{dx}((4x^{2}-13)^{-14})
integral of sin^7(θ)cos(θ)	\int\:\sin^{7}(θ)\cos(θ)dθ
integral of-1/7 x^{-8/7}	\int\:-\frac{1}{7}x^{-\frac{8}{7}}dx
derivative of cot(3x-5)	\frac{d}{dx}(\cot(3x-5))
y^{''}+2y^'-15y=5e^{2t}	y^{\prime\:\prime\:}+2y^{\prime\:}-15y=5e^{2t}
(\partial)/(\partial x)(sin(x+y+z))	\frac{\partial\:}{\partial\:x}(\sin(x+y+z))
integral of (x+16)/(x^2+22x+125)	\int\:\frac{x+16}{x^{2}+22x+125}dx
integral of 9cos^2(xta)n^3x	\int\:9\cos^{2}(xta)n^{3}xdx
(\partial)/(\partial x)(ln(x+2y+3z))	\frac{\partial\:}{\partial\:x}(\ln(x+2y+3z))
limit as x approaches+0+of (1+x)^{2/x}	\lim\:_{x\to\:+0+}((1+x)^{\frac{2}{x}})

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