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Popular Calculus Problems

integral of (24q)/(4q^2+7)	\int\:\frac{24q}{4q^{2}+7}dq
(\partial)/(\partial x)(2x^2y+3xy^3)	\frac{\partial\:}{\partial\:x}(2x^{2}y+3xy^{3})
f^'(x)=((5x+1))/(5x)	f^{\prime\:}(x)=\frac{(5x+1)}{5x}
(\partial)/(\partial x)(msin(2mx+2ny))	\frac{\partial\:}{\partial\:x}(m\sin(2mx+2ny))
integral from 0 to 1 of 2x-x^2	\int\:_{0}^{1}2x-x^{2}dx
(\partial)/(\partial x)(5sin(xy))	\frac{\partial\:}{\partial\:x}(5\sin(xy))
derivative of (x^2/(3+sqrt(x)))	\frac{d}{dx}(\frac{x^{2}}{3+\sqrt{x}})
y^'+6xy^2=0	y^{\prime\:}+6xy^{2}=0
derivative of (1000/x)	\frac{d}{dx}(\frac{1000}{x})
(d^2)/(dx^2)(arctan(x))	\frac{d^{2}}{dx^{2}}(\arctan(x))
derivative of sin^{ln(x}(9x))	\frac{d}{dx}(\sin^{\ln(x)}(9x))
integral of 4/(\sqrt[4]{x^3)}	\int\:\frac{4}{\sqrt[4]{x^{3}}}dx
derivative of arccsc(-4t^2)	derivative\:\arccsc(-4t^{2})
(\partial)/(\partial x)(5x(3+y)^{-1})	\frac{\partial\:}{\partial\:x}(5x(3+y)^{-1})
(d^2)/(dx^2)(7cos(3x))	\frac{d^{2}}{dx^{2}}(7\cos(3x))
derivative of 1-2x-3x^2	\frac{d}{dx}(1-2x-3x^{2})
integral of 1/(x^2(9+x^2))	\int\:\frac{1}{x^{2}(9+x^{2})}dx
integral of 5/(x^2sqrt(x^2+4))	\int\:\frac{5}{x^{2}\sqrt{x^{2}+4}}dx
integral from 16 to x of sqrt(1+9t)	\int\:_{16}^{x}\sqrt{1+9t}dt
derivative of \sqrt[6]{x}	derivative\:\sqrt[6]{x}
(dy)/(dx)=-5sin(4x)	\frac{dy}{dx}=-5\sin(4x)
integral of 9/(x^2+3x-18)	\int\:\frac{9}{x^{2}+3x-18}dx
integral from-3 to 1 of \|3x+3\|	\int\:_{-3}^{1}\left\|3x+3\right\|dx
x^2y^'=2y^2-x^2	x^{2}y^{\prime\:}=2y^{2}-x^{2}
integral of sinh^2(2x)	\int\:\sinh^{2}(2x)dx
derivative of be^θ	derivative\:be^{θ}
(\partial)/(\partial x)(x^2+2y^4+8xy)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{4}+8xy)
integral of 7/(xln(x))	\int\:\frac{7}{x\ln(x)}dx
(\partial)/(\partial x)((x-4)^2+(y-4)^2-5)	\frac{\partial\:}{\partial\:x}((x-4)^{2}+(y-4)^{2}-5)
integral of x/(sqrt(16-9x^4))	\int\:\frac{x}{\sqrt{16-9x^{4}}}dx
integral of (3x^2-10)/(x^2-4x+4)	\int\:\frac{3x^{2}-10}{x^{2}-4x+4}dx
y^{''}-6y^'+13y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+13y=0
(dy)/(dx)=xy^3(1+x^2)^{-1/2},y(0)=1	\frac{dy}{dx}=xy^{3}(1+x^{2})^{-\frac{1}{2}},y(0)=1
(\partial)/(\partial x)(-xy(-15-x-y))	\frac{\partial\:}{\partial\:x}(-xy(-15-x-y))
(\partial)/(\partial x)(3cos(3x+4y))	\frac{\partial\:}{\partial\:x}(3\cos(3x+4y))
(dy)/(dt)= t/(y-2),y(-1)=0	\frac{dy}{dt}=\frac{t}{y-2},y(-1)=0
derivative of 6\sqrt[4]{x^3}	\frac{d}{dx}(6\sqrt[4]{x^{3}})
derivative of 3/(5x^2)	\frac{d}{dx}(\frac{3}{5x^{2}})
integral of sin(x)sin(2x)cos(3x)	\int\:\sin(x)\sin(2x)\cos(3x)dx
(\partial)/(\partial x)((-xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{-xy}{x^{2}+y^{2}})
limit as x approaches 3+of (3-x)/(x^2-9)	\lim\:_{x\to\:3+}(\frac{3-x}{x^{2}-9})
limit as t approaches 1 of (t^2-t)/(t-1)	\lim\:_{t\to\:1}(\frac{t^{2}-t}{t-1})
(d^2)/(dx^2)f(x)=x^3+3x^2-2x+1	\frac{d^{2}}{dx^{2}}f(x)=x^{3}+3x^{2}-2x+1
(\partial)/(\partial x)(2xye^{xz})	\frac{\partial\:}{\partial\:x}(2xye^{xz})
maclaurin x	maclaurin\:x
derivative of 4/3 sin(x)	\frac{d}{dx}(\frac{4}{3}\sin(x))
limit as x approaches 2 of (x^2-8)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{2}-8}{x-2})
2y^{''}+3y^'-y=0	2y^{\prime\:\prime\:}+3y^{\prime\:}-y=0
limit as x approaches 0 of x/(\|x\|+x^2)	\lim\:_{x\to\:0}(\frac{x}{\left\|x\right\|+x^{2}})
inverse oflaplace (e^{-4s})/((s-3)^2)	inverselaplace\:\frac{e^{-4s}}{(s-3)^{2}}
derivative of x^2-6	derivative\:x^{2}-6
derivative of f(x)=x-9	derivative\:f(x)=x-9
integral of 1/(sqrt(-x^2-6x+40))	\int\:\frac{1}{\sqrt{-x^{2}-6x+40}}dx
limit as x approaches 0 of cot^2(x)	\lim\:_{x\to\:0}(\cot^{2}(x))
limit as x approaches 2 of 1/(sqrt(x-2))	\lim\:_{x\to\:2}(\frac{1}{\sqrt{x-2}})
integral of (x^2+4x+1)/(x^3+x)	\int\:\frac{x^{2}+4x+1}{x^{3}+x}dx
derivative of ((x^2-1)/(x^2))	\frac{d}{dx}(\frac{(x^{2}-1)}{x^{2}})
integral of-sin(x)cos^2(x)	\int\:-\sin(x)\cos^{2}(x)dx
derivative of ((1-4x))/(1+4x)	derivative\:\frac{(1-4x)}{1+4x}
3xdy+4ydx=x^2y^2dx	3xdy+4ydx=x^{2}y^{2}dx
derivative of ln(18x)	\frac{d}{dx}(\ln(18x))
integral of 2xsec^2(4x^2)	\int\:2x\sec^{2}(4x^{2})dx
limit as x approaches (pi/2)+of x-pi/2	\lim\:_{x\to\:(\frac{π}{2})+}(x-\frac{π}{2})
d/(d{x)}(4{x}^2{y}+2{z}^3)	\frac{d}{d{x}}(4{x}^{2}{y}+2{z}^{3})
limit as x approaches 0 of (tan(x))^x	\lim\:_{x\to\:0}((\tan(x))^{x})
derivative of f(x)=sqrt(1-e^{cos(1-x^2))}	derivative\:f(x)=\sqrt{1-e^{\cos(1-x^{2})}}
derivative of e^{e-3x}	derivative\:e^{e-3x}
integral of (-5x^4-4\sqrt[3]{x})/(4x)	\int\:\frac{-5x^{4}-4\sqrt[3]{x}}{4x}dx
integral of sqrt(2)	\int\:\sqrt{2}dx
limit as x approaches 3+of (-5)/(x-3)	\lim\:_{x\to\:3+}(\frac{-5}{x-3})
derivative of (e^x/(4-3e^x))	\frac{d}{dx}(\frac{e^{x}}{4-3e^{x}})
(\partial)/(\partial x)(x^2y+x+1)	\frac{\partial\:}{\partial\:x}(x^{2}y+x+1)
maclaurin e^{5x}	maclaurin\:e^{5x}
integral of (x^3e^{-x^2})	\int\:(x^{3}e^{-x^{2}})dx
integral of sin(ln(3x))	\int\:\sin(\ln(3x))dx
derivative of 4/(x^2+2)	\frac{d}{dx}(\frac{4}{x^{2}+2})
integral from 0 to ln(2) of e^{2x}	\int\:_{0}^{\ln(2)}e^{2x}dx
integral of 9/2 (t+1)^{1/2}	\int\:\frac{9}{2}(t+1)^{\frac{1}{2}}dt
y^'=x^3(1-y),y(0)=3	y^{\prime\:}=x^{3}(1-y),y(0)=3
integral of (sqrt(x-1))/(sqrt(x+1))	\int\:\frac{\sqrt{x-1}}{\sqrt{x+1}}dx
laplacetransform e^{-1}	laplacetransform\:e^{-1}
limit as t approaches 0 of e^{-7t}	\lim\:_{t\to\:0}(e^{-7t})
integral of-y/(3+y^2)	\int\:-\frac{y}{3+y^{2}}dy
integral of 1/(2x^2+x+1)	\int\:\frac{1}{2x^{2}+x+1}dx
(\partial)/(\partial x)(t^6e^{-x})	\frac{\partial\:}{\partial\:x}(t^{6}e^{-x})
y^{''}+4y=4x	y^{\prime\:\prime\:}+4y=4x
integral of x^2+5x+1	\int\:x^{2}+5x+1dx
derivative of f(x)=(x-sqrt(1-x^2))^2	\frac{d}{dx}f(x)=(x-\sqrt{1-x^{2}})^{2}
derivative of 12cos(2x+pi/6)	\frac{d}{dx}(12\cos(2x+\frac{π}{6}))
(dy)/(dx)-2y=e^x	\frac{dy}{dx}-2y=e^{x}
derivative of y^2ln(x)	\frac{d}{dx}(y^{2}\ln(x))
limit as t approaches-infinity of e^{3t}	\lim\:_{t\to\:-\infty\:}(e^{3t})
implicit (dy)/(dx),x^2e^y-y^4=e^x	implicit\:\frac{dy}{dx},x^{2}e^{y}-y^{4}=e^{x}
derivative of f(x)=2sin^3(sqrt(x))	derivative\:f(x)=2\sin^{3}(\sqrt{x})
integral of (-4x^5-x^{3/4}-2)/(9x^{4/3)}	\int\:\frac{-4x^{5}-x^{\frac{3}{4}}-2}{9x^{\frac{4}{3}}}dx
integral of 2x(x^2+7)^8	\int\:2x(x^{2}+7)^{8}dx
integral of sqrt(x)(x^3-2x^2)	\int\:\sqrt{x}(x^{3}-2x^{2})dx
derivative of x^2+(2x/(sqrt(x))-1/(x^2))	\frac{d}{dx}(x^{2}+\frac{2x}{\sqrt{x}}-\frac{1}{x^{2}})
integral of cos^3(x/7)	\int\:\cos^{3}(\frac{x}{7})dx
integral of (x+5)ln(x)	\int\:(x+5)\ln(x)dx

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