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Popular Calculus Problems

integral of (5x)/((x-2)^2)	\int\:\frac{5x}{(x-2)^{2}}dx
d/(dθ)(tan(θ/2))	\frac{d}{dθ}(\tan(\frac{θ}{2}))
integral of (x^2-2x+5)	\int\:(x^{2}-2x+5)dx
integral from-8 to 8 of (e^x-e^{-x})^2	\int\:_{-8}^{8}(e^{x}-e^{-x})^{2}dx
integral from 0 to 2 of x+1	\int\:_{0}^{2}x+1dx
integral from 0 to 4 of x-2sqrt(x)	\int\:_{0}^{4}x-2\sqrt{x}dx
integral of-xsqrt(x-1)	\int\:-x\sqrt{x-1}dx
(\partial)/(\partial x)(xln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(x\ln(x^{2}+y^{2}))
(\partial)/(\partial x)(4x(5+y)^{-1})	\frac{\partial\:}{\partial\:x}(4x(5+y)^{-1})
tangent of f(x)=x^3+2x,\at x=0	tangent\:f(x)=x^{3}+2x,\at\:x=0
(\partial)/(\partial x)((-cos(x))/(sqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{-\cos(x)}{\sqrt{x}})
taylor 3^x	taylor\:3^{x}
limit as x approaches 1 of-4x+6	\lim\:_{x\to\:1}(-4x+6)
(dy)/(dx)=e^{2x+3y}	\frac{dy}{dx}=e^{2x+3y}
derivative of 1/6 \sqrt[5]{(6-5x^2^7})	\frac{d}{dx}(\frac{1}{6}\sqrt[5]{(6-5x^{2})^{7}})
integral of x/(\sqrt[3]{x-1)}	\int\:\frac{x}{\sqrt[3]{x-1}}dx
integral of xe^{-1/10 x^2}	\int\:xe^{-\frac{1}{10}x^{2}}dx
(d^3)/(dx^3)((1+sqrt(x))^3)	\frac{d^{3}}{dx^{3}}((1+\sqrt{x})^{3})
(\partial)/(\partial x)(2xy^3+2)	\frac{\partial\:}{\partial\:x}(2xy^{3}+2)
y^'-(3/t)y=2t^3e^{(2t)},y(1)=0	y^{\prime\:}-(\frac{3}{t})\cdot\:y=2t^{3}\cdot\:e^{(2t)},y(1)=0
sum from n=1 to infinity of 1/(2^n-5)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}-5}
derivative of f(x)=(x+2)*sqrt(-x)	derivative\:f(x)=(x+2)\cdot\:\sqrt{-x}
(dy}{dx}=\frac{2y)/x-x^2y^2	\frac{dy}{dx}=\frac{2y}{x}-x^{2}y^{2}
y^{''}+3y^'+2y= 1/(3+e^x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\frac{1}{3+e^{x}}
derivative of sqrt(r)+\sqrt[9]{r}	derivative\:\sqrt{r}+\sqrt[9]{r}
limit as x approaches 1 of sqrt(2x^2-x)	\lim\:_{x\to\:1}(\sqrt{2x^{2}-x})
(dy)/(dx)=x^4(y-2)	\frac{dy}{dx}=x^{4}(y-2)
limit as x approaches 1 of cos(xpi)	\lim\:_{x\to\:1}(\cos(xπ))
derivative of 1/(x^{13)}	derivative\:\frac{1}{x^{13}}
xy^'-2y=-2x^2+x-2	xy^{\prime\:}-2y=-2x^{2}+x-2
tangent of f(x)=6x^2-x^3,\at x=1	tangent\:f(x)=6x^{2}-x^{3},\at\:x=1
factor-sin(x)-4	factor\:-\sin(x)-4
integral of (t)(e^{2t})	\int\:(t)(e^{2t})dt
f(x)=cosh(3*ln(x/2))	f(x)=\cosh(3\cdot\:\ln(\frac{x}{2}))
integral of e^{2x}cos^2(x)	\int\:e^{2x}\cos^{2}(x)dx
f(t)=-sin(t)	f(t)=-\sin(t)
integral of (x^4)/(sqrt((1-x^2)^3))	\int\:\frac{x^{4}}{\sqrt{(1-x^{2})^{3}}}dx
derivative of (x+2)^{2^'}	derivative\:(x+2)^{2^{\prime\:}}
integral of 9e^{2x}	\int\:9e^{2x}dx
integral from 1 to 11x^{15 of} 1/t	\int\:_{1}^{11x^{15}}\frac{1}{t}dt
derivative of (2x^5/(5+3x^4+6x^3+2x+4))	\frac{d}{dx}(\frac{2x^{5}}{5+3x^{4}+6x^{3}+2x+4})
limit as z approaches 0 of (2z-8) 1/3	\lim\:_{z\to\:0}((2z-8)\frac{1}{3})
derivative of (2x/(3-tan(x)))	\frac{d}{dx}(\frac{2x}{3-\tan(x)})
derivative of-3x	derivative\:-3x
(\partial)/(\partial y)(xyln(x^2+y^2))	\frac{\partial\:}{\partial\:y}(xy\ln(x^{2}+y^{2}))
integral of 2/(sqrt(4-x^2))	\int\:\frac{2}{\sqrt{4-x^{2}}}dx
integral of ((x+2))/((x+1))	\int\:\frac{(x+2)}{(x+1)}dx
y^'(t)=(y+1)*(y-3),y(0)=1	y^{\prime\:}(t)=(y+1)\cdot\:(y-3),y(0)=1
integral of 1/2 (x+1/2 sin(2x))	\int\:\frac{1}{2}(x+\frac{1}{2}\sin(2x))dx
limit as x approaches 1 of x^2-2x	\lim\:_{x\to\:1}(x^{2}-2x)
(\partial)/(\partial y)(x^2-5xy+3y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-5xy+3y^{2})
integral of 4x^2-16x+16	\int\:4x^{2}-16x+16dx
limit as x approaches 1 of (x^4-1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{4}-1}{x-1})
tangent of f(-2)=2x^4	tangent\:f(-2)=2x^{4}
derivative of (4x+1^2)	\frac{d}{dx}((4x+1)^{2})
derivative of 1/((1-2x))	\frac{d}{dx}(\frac{1}{(1-2x)})
derivative of e^{4t}	derivative\:e^{4t}
derivative of x^2*e^{-3x}	\frac{d}{dx}(x^{2}\cdot\:e^{-3x})
(e^tx+1)dt+(e^t-1)dx=0,x(1)=1	(e^{t}x+1)dt+(e^{t}-1)dx=0,x(1)=1
limit as x approaches 1 of log_{1/e}(x)	\lim\:_{x\to\:1}(\log_{\frac{1}{e}}(x))
laplacetransform t*e^{5t}sin(3t)	laplacetransform\:t\cdot\:e^{5t}\sin(3t)
(\partial)/(\partial y)(1-xy)	\frac{\partial\:}{\partial\:y}(1-xy)
inverse oflaplace 1/(s(s^2+4))+1	inverselaplace\:\frac{1}{s(s^{2}+4)}+1
limit as x approaches 0 of (4/(x-1)+4)/x	\lim\:_{x\to\:0}(\frac{\frac{4}{x-1}+4}{x})
derivative of sqrt(x/(x+2))	\frac{d}{dx}(\sqrt{\frac{x}{x+2}})
derivative of e^{4xsin(2x)}	derivative\:e^{4x\sin(2x)}
derivative of f(x)=x^3+5x	derivative\:f(x)=x^{3}+5x
(\partial)/(\partial x)(4e^{4xy})	\frac{\partial\:}{\partial\:x}(4e^{4xy})
laplacetransform te^t	laplacetransform\:te^{t}
derivative of e^{x^4}+7x	\frac{d}{dx}(e^{x^{4}}+7x)
normal of f(x)=sqrt(x^2+16),\at x=3	normal\:f(x)=\sqrt{x^{2}+16},\at\:x=3
integral of (e^{8x})/(e^{8x)+6}	\int\:\frac{e^{8x}}{e^{8x}+6}dx
limit as y approaches 1 of (2sqrt(y^2+3))/(y-1)	\lim\:_{y\to\:1}(\frac{2\sqrt{y^{2}+3}}{y-1})
d/(dt)(2e^{-t}t-e^{-t}t^2)	\frac{d}{dt}(2e^{-t}t-e^{-t}t^{2})
derivative of (9x^6+4x^3^4)	\frac{d}{dx}((9x^{6}+4x^{3})^{4})
limit as t approaches pi of sin(3/4 t)	\lim\:_{t\to\:π}(\sin(\frac{3}{4}t))
slope of (-4,7),(2,-8)	slope\:(-4,7),(2,-8)
limit as x approaches 1+of (1-x)*tan((pix)/2)	\lim\:_{x\to\:1+}((1-x)\cdot\:\tan(\frac{πx}{2}))
(\partial)/(\partial y)((x^2y^2)/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}y^{2}}{x+y})
area y^2=x,x-y=2	area\:y^{2}=x,x-y=2
derivative of 2e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(2e^{x}+\frac{2}{\sqrt[3]{x}})
integral of (4x)/((x^2+3)^2)	\int\:\frac{4x}{(x^{2}+3)^{2}}dx
tangent of f(x)= 4/x ,\at x=2	tangent\:f(x)=\frac{4}{x},\at\:x=2
integral of (2-x)/(x^2+x)	\int\:\frac{2-x}{x^{2}+x}dx
integral from 4 to 16 of 1/(8-sqrt(x))	\int\:_{4}^{16}\frac{1}{8-\sqrt{x}}dx
tangent of f(x)=8x^2-x^3,(2,24)	tangent\:f(x)=8x^{2}-x^{3},(2,24)
slope of (3,4),(5,8)	slope\:(3,4),(5,8)
y^'=(2y)/(3x)	y^{\prime\:}=\frac{2y}{3x}
derivative of 1/(2+x)	derivative\:\frac{1}{2+x}
limit as t approaches 0 of (tan(5t))k	\lim\:_{t\to\:0}((\tan(5t))k)
taylor z/(z^{4+9)}	taylor\:\frac{z}{z^{4+9}}
integral of (5x^4)/4+(3x^2)/2+7x+C	\int\:\frac{5x^{4}}{4}+\frac{3x^{2}}{2}+7x+Cdx
inverse oflaplace (s+1)/((s+1)^2+1)	inverselaplace\:\frac{s+1}{(s+1)^{2}+1}
integral of (11x)^2	\int\:(11x)^{2}dx
integral of 1/((x+4)^{7/2)}	\int\:\frac{1}{(x+4)^{\frac{7}{2}}}dx
y^'+2xy=1	y^{\prime\:}+2xy=1
(\partial)/(\partial x)(e^t)	\frac{\partial\:}{\partial\:x}(e^{t})
limit as x approaches 1 of x^3-2x+2	\lim\:_{x\to\:1}(x^{3}-2x+2)
integral of 2/(4x+7sqrt(x))	\int\:\frac{2}{4x+7\sqrt{x}}dx
(dy)/(dt)=y^2+k	\frac{dy}{dt}=y^{2}+k

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