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Popular Calculus Problems

tangent of (2+x)*e^x	tangent\:(2+x)\cdot\:e^{x}
derivative of 2x^2+3x	\frac{d}{dx}(2x^{2}+3x)
d/(dt)(1/(sqrt(t)))	\frac{d}{dt}(\frac{1}{\sqrt{t}})
integral from 0 to 1 of sqrt(1+(x)^2)	\int\:_{0}^{1}\sqrt{1+(x)^{2}}dx
integral from 0 to 6 of 2pi(y+2)(3-y/2)	\int\:_{0}^{6}2π(y+2)(3-\frac{y}{2})dy
limit as x approaches 0-of csc(x)(x-1)	\lim\:_{x\to\:0-}(\csc(x)(x-1))
integral from-infinity to 0 of x^2e^x	\int\:_{-\infty\:}^{0}x^{2}e^{x}dx
integral of 1+1/(2x)	\int\:1+\frac{1}{2x}dx
integral from 1 to 3 of e^x	\int\:_{1}^{3}e^{x}dx
integral from 3 to 6 of x/(x^2+6x+13)	\int\:_{3}^{6}\frac{x}{x^{2}+6x+13}dx
(\partial)/(\partial y)(2x^{4y})	\frac{\partial\:}{\partial\:y}(2x^{4y})
12^'	12^{\prime\:}
limit as x approaches-0 of f(x)	\lim\:_{x\to\:-0}(f(x))
integral from 1 to 5 of (5x-5/x)	\int\:_{1}^{5}(5x-\frac{5}{x})dx
integral of 5tan(x)sec^3(x)	\int\:5\tan(x)\sec^{3}(x)dx
(\partial)/(\partial x)(xy^3+x^2)	\frac{\partial\:}{\partial\:x}(xy^{3}+x^{2})
integral of ln(1+y)	\int\:\ln(1+y)dy
derivative of y=ln(sqrt(x+3))	derivative\:y=\ln(\sqrt{x+3})
y^{''}+9y=-sin(3t)	y^{\prime\:\prime\:}+9y=-\sin(3t)
area y=2x^3+3x^2-4x,y=x^2	area\:y=2x^{3}+3x^{2}-4x,y=x^{2}
derivative of f(x)= 2/(4x+3)	derivative\:f(x)=\frac{2}{4x+3}
integral from 1 to e^2 of (ln^6(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{6}(x^{2})}{x}dx
derivative of f(x)=(x-4)/(x+2)	derivative\:f(x)=\frac{x-4}{x+2}
tangent of x/(sqrt(36+x^2))	tangent\:\frac{x}{\sqrt{36+x^{2}}}
x^2ydy-xy^2dx-x^3y^2dx=0	x^{2}ydy-xy^{2}dx-x^{3}y^{2}dx=0
integral of (2x)/(1+2x^2)	\int\:\frac{2x}{1+2x^{2}}dx
(\partial)/(\partial x)(x^2*e^x)	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:e^{x})
area y=x^2,y= 2/((x^2+1))	area\:y=x^{2},y=\frac{2}{(x^{2}+1)}
xy^'-4y=x^5e^x	xy^{\prime\:}-4y=x^{5}e^{x}
(\partial)/(\partial x)(sqrt(9-x^2-3y))	\frac{\partial\:}{\partial\:x}(\sqrt{9-x^{2}-3y})
derivative of y=arcsin(6x+1)	derivative\:y=\arcsin(6x+1)
integral of 1/(sqrt(-2x^2-12x+32))	\int\:\frac{1}{\sqrt{-2x^{2}-12x+32}}dx
simplify ln(sqrt((a^2-z^2)/(a^2+z^2)))	simplify\:\ln(\sqrt{\frac{a^{2}-z^{2}}{a^{2}+z^{2}}})
limit as x approaches 5 of (x-5)/(x-5)	\lim\:_{x\to\:5}(\frac{x-5}{x-5})
limit as x approaches 1 of 18x^{100}-5	\lim\:_{x\to\:1}(18x^{100}-5)
integral from 1 to 3 of (3x^2+4)	\int\:_{1}^{3}(3x^{2}+4)dx
(dy)/(dx)=(-0.1)/(cos(y)),y(0)= pi/2	\frac{dy}{dx}=\frac{-0.1}{\cos(y)},y(0)=\frac{π}{2}
sum from n=0 to infinity of n*2^{n-1}	\sum\:_{n=0}^{\infty\:}n\cdot\:2^{n-1}
(\partial)/(\partial x)(y^2e^{xyz})	\frac{\partial\:}{\partial\:x}(y^{2}e^{xyz})
limit as x approaches-infinity of-2	\lim\:_{x\to\:-\infty\:}(-2)
(2xy+x^3)y^'= 1/2 x^2y+y^2	(2xy+x^{3})y^{\prime\:}=\frac{1}{2}x^{2}y+y^{2}
(\partial)/(\partial y)(x^3y+e^{xy^2})	\frac{\partial\:}{\partial\:y}(x^{3}y+e^{xy^{2}})
integral from 2 to infinity of 2e^{-2x}	\int\:_{2}^{\infty\:}2e^{-2x}dx
integral of 2bx^3	\int\:2bx^{3}dx
derivative of (5x^2-7(3x^2-2x+1))	\frac{d}{dx}((5x^{2}-7)(3x^{2}-2x+1))
tangent of y= x/(sqrt(4-x)),(3,3)	tangent\:y=\frac{x}{\sqrt{4-x}},(3,3)
-1/(4x^{3/2)}	-\frac{1}{4x^{\frac{3}{2}}}
limit as x approaches-infinity of-x^3	\lim\:_{x\to\:-\infty\:}(-x^{3})
(\partial)/(\partial y)(x^ay^{1-a})	\frac{\partial\:}{\partial\:y}(x^{a}y^{1-a})
limit as x approaches-4 of sqrt(x^2-16)	\lim\:_{x\to\:-4}(\sqrt{x^{2}-16})
derivative of 6sin(x-2/(cos(x)))	\frac{d}{dx}(6\sin(x)-\frac{2}{\cos(x)})
(dy)/(dx)=sqrt(1-y^2)	\frac{dy}{dx}=\sqrt{1-y^{2}}
tangent of f(x)=sqrt(6x),(6,6)	tangent\:f(x)=\sqrt{6x},(6,6)
(\partial}{\partial s}(\frac{(s-3r))/t)	\frac{\partial\:}{\partial\:s}(\frac{(s-3r)}{t})
integral of x^2sqrt(13x-1)	\int\:x^{2}\sqrt{13x-1}dx
integral of-1/(2y)	\int\:-\frac{1}{2y}dy
tangent of y= 1/(x^3),(-2,-1/8)	tangent\:y=\frac{1}{x^{3}},(-2,-\frac{1}{8})
limit as x approaches 3+of (1-2x)/(x-3)	\lim\:_{x\to\:3+}(\frac{1-2x}{x-3})
derivative of cot(x/2)	\frac{d}{dx}(\cot(\frac{x}{2}))
(\partial)/(\partial x)(8y-(x+y)^3)	\frac{\partial\:}{\partial\:x}(8y-(x+y)^{3})
derivative of (2x+1/(1-x))	\frac{d}{dx}(\frac{2x+1}{1-x})
integral of 1/(sqrt(4x^2-1))	\int\:\frac{1}{\sqrt{4x^{2}-1}}dx
derivative of xcos(y)	\frac{d}{dx}(x\cos(y))
integral from 0 to 10 of 2200e^{0.024x}-1460e^{0.018x}	\int\:_{0}^{10}2200e^{0.024x}-1460e^{0.018x}dx
integral of 1/T	\int\:\frac{1}{T}dT
derivative of sin^2(5x-3)	\frac{d}{dx}(\sin^{2}(5x-3))
sum from n=0 to infinity of 12^nx^n	\sum\:_{n=0}^{\infty\:}12^{n}x^{n}
derivative of (3x^4(2x^5))	\frac{d}{dx}((3x^{4})(2x^{5}))
integral of e^{3x-5}	\int\:e^{3x-5}dx
y^{'''}-5y^{''}+6y^'+12y=0	y^{\prime\:\prime\:\prime\:}-5y^{\prime\:\prime\:}+6y^{\prime\:}+12y=0
integral of 1/(x^8+x^6)	\int\:\frac{1}{x^{8}+x^{6}}dx
limit as x approaches 0+of x(ln(4x))^2	\lim\:_{x\to\:0+}(x(\ln(4x))^{2})
y^{''}+4y^'+3y=e^x	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=e^{x}
derivative of 9x^2-2x+1	\frac{d}{dx}(9x^{2}-2x+1)
derivative of xsqrt(a^2+x^2)	\frac{d}{dx}(x\sqrt{a^{2}+x^{2}})
area x=y^2-1,x=1-y^2	area\:x=y^{2}-1,x=1-y^{2}
inverse oflaplace 2/(s^2(s+2))	inverselaplace\:\frac{2}{s^{2}(s+2)}
integral of (16x)/(sqrt(8x^2+1))	\int\:\frac{16x}{\sqrt{8x^{2}+1}}dx
integral of sin(7t)	\int\:\sin(7t)dt
derivative of sqrt(x)+1/(\sqrt[3]{x^4})	\frac{d}{dx}(\sqrt{x}+\frac{1}{\sqrt[3]{x^{4}}})
(\partial)/(\partial x)(-e^{-y/x})	\frac{\partial\:}{\partial\:x}(-e^{-\frac{y}{x}})
integral of 1/((x^2)^2)x^2)^2	\int\:\frac{1}{(x^{2})^{2}}d(x^{2})^{2}
derivative of e^{2x^6}-1	\frac{d}{dx}(e^{2x^{6}}-1)
(\partial)/(\partial y)(x^2+y^2+xy)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}+xy)
derivative of (10/((1-x)^3))	\frac{d}{dx}(\frac{10}{(1-x)^{3}})
integral of (-6/(x^4))	\int\:(-\frac{6}{x^{4}})dx
derivative of 2^t	derivative\:2^{t}
integral of (8x-2)/(x^2-1)	\int\:\frac{8x-2}{x^{2}-1}dx
integral of e^{sqrt(9x)}	\int\:e^{\sqrt{9x}}dx
area y=x^3-x,y=3x,-2,2	area\:y=x^{3}-x,y=3x,-2,2
derivative of (1+3x^2(x-x^2))	\frac{d}{dx}((1+3x^{2})(x-x^{2}))
integral of 1/(x(x+4)^2)	\int\:\frac{1}{x(x+4)^{2}}dx
integral from 1 to 3 of \sqrt[3]{x}(x-4)	\int\:_{1}^{3}\sqrt[3]{x}(x-4)dx
implicit (dy)/(dx),e^{4x}=sin(x+5y)	implicit\:\frac{dy}{dx},e^{4x}=\sin(x+5y)
derivative of (e^x)/(1+x)	derivative\:\frac{e^{x}}{1+x}
integral of (sin(x))/(1+cos^2(x))	\int\:\frac{\sin(x)}{1+\cos^{2}(x)}dx
derivative of x^3-7x^2	\frac{d}{dx}(x^{3}-7x^{2})
integral of x(x^2-4)^2	\int\:x(x^{2}-4)^{2}dx
derivative of (x+2/(x^2+4x+13))	\frac{d}{dx}(\frac{x+2}{x^{2}+4x+13})
(\partial)/(\partial y)((x^2+y^2+z^2)^{-1/2})	\frac{\partial\:}{\partial\:y}((x^{2}+y^{2}+z^{2})^{-\frac{1}{2}})

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