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Popular Calculus Problems

integral from-4 to 0 of 2+sqrt(16-x^2)	\int\:_{-4}^{0}2+\sqrt{16-x^{2}}dx
integral from-1 to 2 of x-x^2+2	\int\:_{-1}^{2}x-x^{2}+2dx
(\partial)/(\partial x)(sqrt(2x^2+4y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2x^{2}+4y^{2}})
f(t)=e^{5t}	f(t)=e^{5t}
integral of sin^2(1)	\int\:\sin^{2}(1)dx
(\partial)/(\partial y)(-1/(x^2y))	\frac{\partial\:}{\partial\:y}(-\frac{1}{x^{2}y})
integral from 2 to 4 of x^2((2x-3)/6)	\int\:_{2}^{4}x^{2}(\frac{2x-3}{6})dx
integral from 0 to 1 of 6^{2x}	\int\:_{0}^{1}6^{2x}dx
(\partial)/(\partial x)(12xe^{x-3y})	\frac{\partial\:}{\partial\:x}(12xe^{x-3y})
limit as x approaches 0 of (x+1)sin(1/x)	\lim\:_{x\to\:0}((x+1)\sin(\frac{1}{x}))
derivative of cos^{12}(x)	\frac{d}{dx}(\cos^{12}(x))
derivative of sqrt(5t)+(sqrt(7))/t	derivative\:\sqrt{5t}+\frac{\sqrt{7}}{t}
integral of 1/(3^{-x)}	\int\:\frac{1}{3^{-x}}dx
integral of cos(5x+7)	\int\:\cos(5x+7)dx
f(x)=(x^2-2)/(x^2+2)	f(x)=\frac{x^{2}-2}{x^{2}+2}
(\partial)/(\partial x)((x+y)ln(x/y))	\frac{\partial\:}{\partial\:x}((x+y)\ln(\frac{x}{y}))
integral from 0 to 1 of (47)/(4y-1)	\int\:_{0}^{1}\frac{47}{4y-1}dy
y^'=3-6x+y-2xy	y^{\prime\:}=3-6x+y-2xy
tangent of 1/((1+x^2))	tangent\:\frac{1}{(1+x^{2})}
derivative of sin(x^7)	\frac{d}{dx}(\sin(x^{7}))
derivative of \sqrt[7]{2x^2-1}	\frac{d}{dx}(\sqrt[7]{2x^{2}-1})
integral of sin(3x)+cos(5x)	\int\:\sin(3x)+\cos(5x)dx
derivative of y=e^{-7/(t^2)}	derivative\:y=e^{-\frac{7}{t^{2}}}
derivative of y=-3x+2	derivative\:y=-3x+2
inverse oflaplace (3s+3)/(s^2-9)	inverselaplace\:\frac{3s+3}{s^{2}-9}
taylor-x^4-x^2	taylor\:-x^{4}-x^{2}
(\partial)/(\partial x)(sqrt(2(x+c)))	\frac{\partial\:}{\partial\:x}(\sqrt{2(x+c)})
laplacetransform 4e^{-3t}	laplacetransform\:4e^{-3t}
(dy)/(dx)+5y=e^xy^{-4}	\frac{dy}{dx}+5y=e^{x}y^{-4}
integral of 7/(3x^2+x+2)	\int\:\frac{7}{3x^{2}+x+2}dx
integral of 3t^3	\int\:3t^{3}dt
xy^2dx-x^2y^2dy=0	xy^{2}dx-x^{2}y^{2}dy=0
derivative of e^{((-x^2)/2})	\frac{d}{dx}(e^{\frac{(-x^{2})}{2}})
integral of 1/(sqrt(16-t^2))	\int\:\frac{1}{\sqrt{16-t^{2}}}dt
derivative of f(x)=ln(1+x)	derivative\:f(x)=\ln(1+x)
derivative of ln((sqrt(2x)/(sin(x))))	\frac{d}{dx}(\ln(\frac{\sqrt{2x}}{\sin(x)}))
derivative of y= 3/(sin(2x))	derivative\:y=\frac{3}{\sin(2x)}
limit as x approaches 1 of ((x+3))/2	\lim\:_{x\to\:1}(\frac{(x+3)}{2})
integral of (ax+b)^n	\int\:(ax+b)^{n}dx
integral of sqrt(27-6x-x^2)	\int\:\sqrt{27-6x-x^{2}}dx
derivative of e^{3x}*cos(2x)	\frac{d}{dx}(e^{3x}\cdot\:\cos(2x))
(dy)/(dx)+y^5x+9y=0	\frac{dy}{dx}+y^{5}x+9y=0
integral of 7/(x^5)	\int\:\frac{7}{x^{5}}dx
derivative of x^3+1/(12x)	derivative\:x^{3}+\frac{1}{12x}
limit as x approaches 5 of 1/(x^2-25)	\lim\:_{x\to\:5}(\frac{1}{x^{2}-25})
tangent of f(x)=x^{cos(x)},\at x=pi	tangent\:f(x)=x^{\cos(x)},\at\:x=π
integral of-3sqrt(x)+2x	\int\:-3\sqrt{x}+2xdx
derivative of sqrt(x)+\sqrt[9]{x}	derivative\:\sqrt{x}+\sqrt[9]{x}
integral of (11-x)	\int\:(11-x)dx
limit as x approaches 5+of 3/(x-5)	\lim\:_{x\to\:5+}(\frac{3}{x-5})
integral from 0 to pi/(12) of 6tan(3x)	\int\:_{0}^{\frac{π}{12}}6\tan(3x)dx
(\partial)/(\partial x)(aln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(a\ln(x^{2}+y^{2}))
limit as x approaches 2 of 2x^3-3x^2+4x-9	\lim\:_{x\to\:2}(2x^{3}-3x^{2}+4x-9)
y^{''}+2y^'+y=xe^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=xe^{-x}
derivative of (2x^2-6^{-10})	\frac{d}{dx}((2x^{2}-6)^{-10})
limit as x approaches 0 of 3/(x(x+3)^2)	\lim\:_{x\to\:0}(\frac{3}{x(x+3)^{2}})
integral from 1 to e of xln(x)	\int\:_{1}^{e}x\ln(x)dx
(d^2y)/(dx^2)-y=0	\frac{d^{2}y}{dx^{2}}-y=0
limit as x approaches 0 of 3(x)^{x/2}	\lim\:_{x\to\:0}(3(x)^{\frac{x}{2}})
inverse oflaplace ((2s+5))/(s^2+6s+34)	inverselaplace\:\frac{(2s+5)}{s^{2}+6s+34}
integral of xe^{x+2}	\int\:xe^{x+2}dx
sum from n=1 to infinity of ((x-1)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(x-1)^{n}}{n}
derivative of \sqrt[6]{t}-6e^t	derivative\:\sqrt[6]{t}-6e^{t}
integral of cos^2(x)sin^3(x)	\int\:\cos^{2}(x)\sin^{3}(x)dx
integral of sin^4(y)cos^7(y)	\int\:\sin^{4}(y)\cos^{7}(y)dy
implicit (d^2y)/(dx^2),x^2+y^2=36	implicit\:\frac{d^{2}y}{dx^{2}},x^{2}+y^{2}=36
t(dy)/(dt)+27y= 1/t	t\frac{dy}{dt}+27y=\frac{1}{t}
derivative of (2d/(x^3)-a)	\frac{d}{dx}(\frac{2d}{x^{3}}-a)
derivative of f(x)=(10x+x^2)/((5+x)^2)	derivative\:f(x)=\frac{10x+x^{2}}{(5+x)^{2}}
(dy}{dx}-\frac{2x^3)/y =0	\frac{dy}{dx}-\frac{2x^{3}}{y}=0
integral of (10)/(sqrt(9-16x^2))	\int\:\frac{10}{\sqrt{9-16x^{2}}}dx
integral of 1/(sqrt(x^2+4x-12))	\int\:\frac{1}{\sqrt{x^{2}+4x-12}}dx
y^{''}+6y^'+8y=0,y(0)=9	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=0,y(0)=9
derivative of cos(e^{-4θ^5})	derivative\:\cos(e^{-4θ^{5}})
derivative of (9x^2-6/(x^2))	\frac{d}{dx}(\frac{9x^{2}-6}{x^{2}})
(\partial)/(\partial x)(4/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{4}{1+x^{2}})
derivative of 1-xycos(piy)	\frac{d}{dx}(1-xy\cos(πy))
f(x)=5^xln(5)	f(x)=5^{x}\ln(5)
derivative of (1+x^4)^{4/5}	derivative\:(1+x^{4})^{\frac{4}{5}}
integral of ((y-2))/((y+3))	\int\:\frac{(y-2)}{(y+3)}dy
integral of 7/2 x^2	\int\:\frac{7}{2}x^{2}dx
integral of 24x(6x^2+7)^7	\int\:24x(6x^{2}+7)^{7}dx
derivative of 4cos(2x)	derivative\:4\cos(2x)
derivative of (x-5(x+4)(x+6))	\frac{d}{dx}((x-5)(x+4)(x+6))
integral from 0 to 2 of x^2+1	\int\:_{0}^{2}x^{2}+1dx
slope of (5.9)(-4.6)	slope\:(5.9)(-4.6)
(\partial)/(\partial z)(xye^z)	\frac{\partial\:}{\partial\:z}(xye^{z})
normal of y=x^3-3x+2,(2,4)	normal\:y=x^{3}-3x+2,(2,4)
integral of 1/(xsqrt(16x^2-36))	\int\:\frac{1}{x\sqrt{16x^{2}-36}}dx
integral of+1/(7x^5)	\int\:+\frac{1}{7x^{5}}dx
integral from 0 to pi/6 of (tan(x))^2	\int\:_{0}^{\frac{π}{6}}(\tan(x))^{2}dx
integral of cos^3(u)sin^2(u)	\int\:\cos^{3}(u)\sin^{2}(u)du
integral of (x^2+1)/(x^2-1)	\int\:\frac{x^{2}+1}{x^{2}-1}dx
(\partial)/(\partial x)(-3/(x^2))	\frac{\partial\:}{\partial\:x}(-\frac{3}{x^{2}})
implicit (dy)/(dx),y=x^{-10cos(x)}	implicit\:\frac{dy}{dx},y=x^{-10\cos(x)}
tangent of f(x)=(x^2-1)/(x^2+x+1),(1,0)	tangent\:f(x)=\frac{x^{2}-1}{x^{2}+x+1},(1,0)
(1+x)(dy)/(dx)-xy=x+x^2	(1+x)\frac{dy}{dx}-xy=x+x^{2}
derivative of x^{8y}	\frac{d}{dx}(x^{8y})
area y=arcsin(2x),x=(sqrt(3))/4	area\:y=\arcsin(2x),x=\frac{\sqrt{3}}{4}
y^'=(y+5)(x+2)	y^{\prime\:}=(y+5)(x+2)

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