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Popular Calculus Problems

(dy)/(dt)=t^2+13t^2y	\frac{dy}{dt}=t^{2}+13t^{2}y
integral of (e^x+xcos(y))	\int\:(e^{x}+x\cos(y))dy
integral of (x^4)/(sqrt(x^{10)-1)}	\int\:\frac{x^{4}}{\sqrt{x^{10}-1}}dx
derivative of f(x)= 7/(sqrt(x-6))	derivative\:f(x)=\frac{7}{\sqrt{x-6}}
roots e^{kx}	roots\:e^{kx}
(\partial)/(\partial x)(2x^2+4y+1)	\frac{\partial\:}{\partial\:x}(2x^{2}+4y+1)
integral of (3x-x^3+1)/(x^4)	\int\:\frac{3x-x^{3}+1}{x^{4}}dx
derivative of x^2+1	derivative\:x^{2}+1
limit as x approaches 0-of (sin(2x))/x	\lim\:_{x\to\:0-}(\frac{\sin(2x)}{x})
integral of (x^3-3x^2+5x-3)/(x-1)	\int\:\frac{x^{3}-3x^{2}+5x-3}{x-1}dx
area y=3x-x^2,y=-5x	area\:y=3x-x^{2},y=-5x
tangent of f(x)=sqrt(3x+1),\at x=5	tangent\:f(x)=\sqrt{3x+1},\at\:x=5
derivative of 2e^{6x}	\frac{d}{dx}(2e^{6x})
integral of xsqrt(1+x^4)	\int\:x\sqrt{1+x^{4}}dx
derivative of sin^2(x-3y)	\frac{d}{dx}(\sin^{2}(x-3y))
integral of e^xsqrt(3-e^x)	\int\:e^{x}\sqrt{3-e^{x}}dx
integral of 3(x-1)y^3e^{y(1-x)}	\int\:3(x-1)y^{3}e^{y(1-x)}dx
limit as x approaches 1 of ln(x^{1/2})	\lim\:_{x\to\:1}(\ln(x^{\frac{1}{2}}))
inverse oflaplace 1/(s^3+5s)	inverselaplace\:\frac{1}{s^{3}+5s}
inverse oflaplace 1/(1+sa)	inverselaplace\:\frac{1}{1+sa}
derivative of f(x)=8^{(x^2+4x)}	\frac{d}{dx}f(x)=8^{(x^{2}+4x)}
(dy)/(dx)=e^{2x+3y},y(0)=0	\frac{dy}{dx}=e^{2x+3y},y(0)=0
integral from 6 to infinity of xe^{-2x}	\int\:_{6}^{\infty\:}xe^{-2x}dx
integral of-5cos(x)	\int\:-5\cos(x)dx
integral of 8sec^2(x)	\int\:8\sec^{2}(x)dx
limit as x approaches 3 of f(x)(g(x))	\lim\:_{x\to\:3}(f(x)(g(x)))
dy=(y-1)^2dx	dy=(y-1)^{2}dx
limit as x approaches 2 of (sqrt(x^2-4x)-2x)/(2x+5)	\lim\:_{x\to\:2}(\frac{\sqrt{x^{2}-4x}-2x}{2x+5})
y^'-y^2+0.5-20y=0	y^{\prime\:}-y^{2}+0.5-20y=0
(\partial)/(\partial y)(((x+y))/(x-y))	\frac{\partial\:}{\partial\:y}(\frac{(x+y)}{x-y})
integral of 1/(sin(x)cos(x)+cos^2(x))	\int\:\frac{1}{\sin(x)\cos(x)+\cos^{2}(x)}dx
integral of (cos(x))/(1-sin(x))	\int\:\frac{\cos(x)}{1-\sin(x)}dx
sum from n=0 to infinity of 1/((4n^2-1))	\sum\:_{n=0}^{\infty\:}\frac{1}{(4n^{2}-1)}
derivative of sin^3(x+sin(3x))	\frac{d}{dx}(\sin^{3}(x)+\sin(3x))
d/(dy)(sqrt(tan(x)+y))	\frac{d}{dy}(\sqrt{\tan(x)+y})
derivative of x^{(-1/2})	\frac{d}{dx}(x^{\frac{-1}{2}})
inverse oflaplace 1/((s-4))	inverselaplace\:\frac{1}{(s-4)}
(\partial)/(\partial y)(x^2yz+1/(xyz^2))	\frac{\partial\:}{\partial\:y}(x^{2}yz+\frac{1}{xyz^{2}})
(dy)/(dx)=5y^2,y(0)=3	\frac{dy}{dx}=5y^{2},y(0)=3
tangent of f(x)=x^3-15x,(1,-14)	tangent\:f(x)=x^{3}-15x,(1,-14)
tangent of 1/(sqrt(5x)),\at x=9	tangent\:\frac{1}{\sqrt{5x}},\at\:x=9
taylor 1/((sqrt((3-2x))))	taylor\:\frac{1}{(\sqrt{(3-2x)})}
tangent of (5x+2)/(6x-4)	tangent\:\frac{5x+2}{6x-4}
integral from 0 to 4 of 2t+4	\int\:_{0}^{4}2t+4dt
area x+y=4,x-y=0,y+3x=4	area\:x+y=4,x-y=0,y+3x=4
derivative of (4x/(x^2-4))	\frac{d}{dx}(\frac{4x}{x^{2}-4})
(dy)/(dx)+y=e^x	\frac{dy}{dx}+y=e^{x}
derivative of (x+1^{2/3}(2x^2-1)^3)	\frac{d}{dx}((x+1)^{\frac{2}{3}}(2x^{2}-1)^{3})
derivative of sin(kx)	\frac{d}{dx}(\sin(kx))
limit as x approaches-1 of (x-1)/(x+1)	\lim\:_{x\to\:-1}(\frac{x-1}{x+1})
integral of sin^5(x/2)	\int\:\sin^{5}(\frac{x}{2})dx
limit as x approaches 0 of sqrt(5-2x^2)	\lim\:_{x\to\:0}(\sqrt{5-2x^{2}})
limit as x approaches 3 of 2x^{-1}	\lim\:_{x\to\:3}(2x^{-1})
(dy)/(dx)= 1/4 sqrt(y)cos^2(sqrt(y))	\frac{dy}{dx}=\frac{1}{4}\sqrt{y}\cos^{2}(\sqrt{y})
integral of csc(x)tan(x)	\int\:\csc(x)\tan(x)dx
derivative of cos(xln(x^2+1))	\frac{d}{dx}(\cos(x)\ln(x^{2}+1))
limit as x approaches 1+of (1-x)/(x^2-1)	\lim\:_{x\to\:1+}(\frac{1-x}{x^{2}-1})
derivative of y= x/(sqrt(x^2+4))	derivative\:y=\frac{x}{\sqrt{x^{2}+4}}
(\partial)/(\partial y)((xy)/(x+y+z))	\frac{\partial\:}{\partial\:y}(\frac{xy}{x+y+z})
(\partial)/(\partial y)(2xy-y)	\frac{\partial\:}{\partial\:y}(2xy-y)
derivative of (sin(x))/(cos(x))	derivative\:\frac{\sin(x)}{\cos(x)}
d/(dt)(sin(3ln(t)-e^{t^2}))	\frac{d}{dt}(\sin(3\ln(t)-e^{t^{2}}))
tangent of y=x^2-3,(-2,1)	tangent\:y=x^{2}-3,(-2,1)
integral of (x^5+1)/(x^3-3x^2-10x)	\int\:\frac{x^{5}+1}{x^{3}-3x^{2}-10x}dx
derivative of e^xx+7e^x	\frac{d}{dx}(e^{x}x+7e^{x})
integral of (e^x-3)^2	\int\:(e^{x}-3)^{2}dx
area 10x^4-10x^2,9x^2	area\:10x^{4}-10x^{2},9x^{2}
(\partial)/(\partial y)((2-x)(y-2)(3-x-y))	\frac{\partial\:}{\partial\:y}((2-x)(y-2)(3-x-y))
integral of 2/(x^2+x)	\int\:\frac{2}{x^{2}+x}dx
derivative of (6x^2+8x+4/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+8x+4}{\sqrt{x}})
derivative of (x^{x+1})	\frac{d}{dx}((x)^{x+1})
(dx)/(dy)=sin(x+y)	\frac{dx}{dy}=\sin(x+y)
y^'=-ay	y^{\prime\:}=-ay
derivative of x^ay^{1-a}	\frac{d}{dx}(x^{a}y^{1-a})
slope of (1,-1),(6,-1)	slope\:(1,-1),(6,-1)
integral from 6 to 8 of (92)/((x-6)^3)	\int\:_{6}^{8}\frac{92}{(x-6)^{3}}dx
derivative of sin^4(cos(8x))	\frac{d}{dx}(\sin^{4}(\cos(8x)))
limit as x approaches 4 of x^4-5x^2+2	\lim\:_{x\to\:4}(x^{4}-5x^{2}+2)
area f(x)= 1/x ,[1,2]	area\:f(x)=\frac{1}{x},[1,2]
integral from-5 to 0 of 2^{1-x}	\int\:_{-5}^{0}2^{1-x}dx
tangent of y=(6x)/(x^2+1)	tangent\:y=\frac{6x}{x^{2}+1}
(\partial)/(\partial x)(xsin(2y))	\frac{\partial\:}{\partial\:x}(x\sin(2y))
derivative of f(x)=(x^2+3)(x^2-4x)	derivative\:f(x)=(x^{2}+3)(x^{2}-4x)
integral of (2x+6)e^{-4x}	\int\:(2x+6)e^{-4x}dx
derivative of 7(cos(x^2-2x^2sin(x^2)))	\frac{d}{dx}(7(\cos(x^{2})-2x^{2}\sin(x^{2})))
derivative of f(x)=x^22^x	derivative\:f(x)=x^{2}2^{x}
integral of 5/(x^2+4x-1)	\int\:\frac{5}{x^{2}+4x-1}dx
integral of 1/(x(x^2+1))	\int\:\frac{1}{x(x^{2}+1)}dx
derivative of cos(e^{-t^2})	derivative\:\cos(e^{-t^{2}})
integral from 0 to pi of sin(6x)cos(3x)	\int\:_{0}^{π}\sin(6x)\cos(3x)dx
integral of-2e^x(e^x-1)^3	\int\:-2e^{x}(e^{x}-1)^{3}dx
derivative of 9arctan(x-sqrt(1+x^2))	derivative\:9\arctan(x-\sqrt{1+x^{2}})
slope of (19,-16),(-7,-15)	slope\:(19,-16),(-7,-15)
limit as x approaches 2 of x^3	\lim\:_{x\to\:2}(x^{3})
derivative of 7xe^x	derivative\:7xe^{x}
(\partial)/(\partial y)(-y/((x+2)^2))	\frac{\partial\:}{\partial\:y}(-\frac{y}{(x+2)^{2}})
derivative of (x^2+1/(3x^3+4x))	\frac{d}{dx}(\frac{x^{2}+1}{3x^{3}+4x})
integral of (e^{sqrt(x)})	\int\:(e^{\sqrt{x}})dx
derivative of (x-4/(x+2))	\frac{d}{dx}(\frac{x-4}{x+2})
integral of 8e^x	\int\:8e^{x}dx

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