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Popular Calculus Problems

y^'=(3x-2)^2(30x+29)	y^{\prime\:}=(3x-2)^{2}(30x+29)
ty^'+(t+1)y=2te^{-t}	ty^{\prime\:}+(t+1)y=2te^{-t}
inverse oflaplace (2s+12)/(s^2+6s+18)	inverselaplace\:\frac{2s+12}{s^{2}+6s+18}
integral of (5x^3-4x)/(sqrt(1-x^4))	\int\:\frac{5x^{3}-4x}{\sqrt{1-x^{4}}}dx
integral from 0 to 1 of (x-7)/(x^2-5x+6)	\int\:_{0}^{1}\frac{x-7}{x^{2}-5x+6}dx
y^'+6y=e^{4t}	y^{\prime\:}+6y=e^{4t}
derivative of sec^5(sqrt(x^2-1))	\frac{d}{dx}(\sec^{5}(\sqrt{x^{2}-1}))
derivative of sqrt(3x^2+1)	derivative\:\sqrt{3x^{2}+1}
f(x)=x^{1/9}	f(x)=x^{\frac{1}{9}}
tangent of f(x)=2x(2-4x)^4,\at x=1	tangent\:f(x)=2x(2-4x)^{4},\at\:x=1
derivative of \sqrt[x-2]{2}	\frac{d}{dx}(\sqrt[x-2]{2})
integral of (tan^2(x))/(sec^3(x))	\int\:\frac{\tan^{2}(x)}{\sec^{3}(x)}dx
(t^2+1)(dy)/(dt)=2y	(t^{2}+1)\frac{dy}{dt}=2y
(\partial)/(\partial x)(x^8+8xy^7)	\frac{\partial\:}{\partial\:x}(x^{8}+8xy^{7})
integral of 1^3	\int\:1dx^{3}
f(x)=(x^2)/(ln(x))	f(x)=\frac{x^{2}}{\ln(x)}
derivative of 2x^2-6x	\frac{d}{dx}(2x^{2}-6x)
integral of 4x^{-1}	\int\:4x^{-1}dx
(\partial)/(\partial x)(e^{6xy})	\frac{\partial\:}{\partial\:x}(e^{6xy})
integral from 3 to 5 of 8x^{-3}	\int\:_{3}^{5}8x^{-3}dx
integral from 1 to 7 of w^2ln(w)	\int\:_{1}^{7}w^{2}\ln(w)dw
derivative of 4x^2+3x	derivative\:4x^{2}+3x
integral from 9 to 18 of sqrt(324-x^2)	\int\:_{9}^{18}\sqrt{324-x^{2}}dx
integral of cot(11x)	\int\:\cot(11x)dx
derivative of 2/(sqrt(1+4x))	\frac{d}{dx}(\frac{2}{\sqrt{1+4x}})
slope of (16,-2),(15,86)	slope\:(16,-2),(15,86)
derivative of-(200)/((t+2)^2)	derivative\:-\frac{200}{(t+2)^{2}}
derivative of 3/x+5sin(x)	\frac{d}{dx}(\frac{3}{x}+5\sin(x))
inverse oflaplace 3/(2(s+1)^2+32)	inverselaplace\:\frac{3}{2(s+1)^{2}+32}
integral of tan^4(6x)	\int\:\tan^{4}(6x)dx
derivative of sqrt(5x+3)	derivative\:\sqrt{5x+3}
integral of (10)/(x-5)	\int\:\frac{10}{x-5}dx
tangent of f(x)=2x^2-7x+5,\at x=3	tangent\:f(x)=2x^{2}-7x+5,\at\:x=3
integral from 0 to t of cos(x^2)	\int\:_{0}^{t}\cos(x^{2})dx
(\partial)/(\partial x)(cos(4θ))	\frac{\partial\:}{\partial\:x}(\cos(4θ))
integral of (sin^2(x))/(1+cos(x))	\int\:\frac{\sin^{2}(x)}{1+\cos(x)}dx
derivative of y=x+cos(x)	derivative\:y=x+\cos(x)
derivative of x/1	\frac{d}{dx}(\frac{x}{1})
derivative of f(x)=(12x)/(1-x)	derivative\:f(x)=\frac{12x}{1-x}
(dy)/(dx)=y(1-y^2)	\frac{dy}{dx}=y(1-y^{2})
derivative of f(x)= 1/(\sqrt[3]{x^2-1)}	derivative\:f(x)=\frac{1}{\sqrt[3]{x^{2}-1}}
(\partial)/(\partial x)(ysin(3x))	\frac{\partial\:}{\partial\:x}(y\sin(3x))
integral of (-8x+5)/(x^3+4x)	\int\:\frac{-8x+5}{x^{3}+4x}dx
limit as x approaches 36 of x^{3/2}	\lim\:_{x\to\:36}(x^{\frac{3}{2}})
y^{''}+x=7y	y^{\prime\:\prime\:}+x=7y
(\partial)/(\partial y)(2xe^{-2xy})	\frac{\partial\:}{\partial\:y}(2xe^{-2xy})
(\partial)/(\partial x)(z^2x)	\frac{\partial\:}{\partial\:x}(z^{2}x)
parity sqrt(x+\sqrt{x+\sqrt{x)}}	parity\:\sqrt{x+\sqrt{x+\sqrt{x}}}
y^{''}+6y^'+5y=12te^{5t}	y^{\prime\:\prime\:}+6y^{\prime\:}+5y=12te^{5t}
limit as x approaches 2 of 4x^2+3	\lim\:_{x\to\:2}(4x^{2}+3)
limit as x approaches 1 of 2x^2+1	\lim\:_{x\to\:1}(2x^{2}+1)
(dy)/(dx)-y-e^{3x}=0	\frac{dy}{dx}-y-e^{3x}=0
tangent of f(x)=x^4-20x^2+64,\at x=-1	tangent\:f(x)=x^{4}-20x^{2}+64,\at\:x=-1
limit as x approaches 3 of \|x\|	\lim\:_{x\to\:3}(\left\|x\right\|)
tangent of ((4x^2))/((2-2x)^3)	tangent\:\frac{(4x^{2})}{(2-2x)^{3}}
(dy)/(dx)= x/(42+x^2)	\frac{dy}{dx}=\frac{x}{42+x^{2}}
integral from 1 to 1000 of 1/(x^2)	\int\:_{1}^{1000}\frac{1}{x^{2}}dx
integral of (y+1)x^2	\int\:(y+1)x^{2}
derivative of sin(pit)	derivative\:\sin(πt)
area y=8sqrt(x),y=8x^3	area\:y=8\sqrt{x},y=8x^{3}
derivative of sin(y+xy-x^3)	\frac{d}{dx}(\sin(y)+xy-x^{3})
derivative of (x+1^{ln(x)})	\frac{d}{dx}((x+1)^{\ln(x)})
y^{''}+2y^'=2x+7-e^{-2x}	y^{\prime\:\prime\:}+2y^{\prime\:}=2x+7-e^{-2x}
integral from-1 to 1 of (x^2-1)^2	\int\:_{-1}^{1}(x^{2}-1)^{2}dx
integral of (sqrt(x)-1)/(sqrt(x))	\int\:\frac{\sqrt{x}-1}{\sqrt{x}}dx
6xy^'+y=x^4	6xy^{\prime\:}+y=x^{4}
derivative of e^x(3x+1^3)	\frac{d}{dx}(e^{x}(3x+1)^{3})
derivative of (e^x/y)	\frac{d}{dx}(\frac{e^{x}}{y})
derivative of f(x)=3x^2-ln(x)	derivative\:f(x)=3x^{2}-\ln(x)
taylor 2/x ,3	taylor\:\frac{2}{x},3
x^2y^{''}+xy^'-y= 1/x	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=\frac{1}{x}
(dy)/(dx)=((4y+3)/(8x+5))^2	\frac{dy}{dx}=(\frac{4y+3}{8x+5})^{2}
integral of cos(x^2)x	\int\:\cos(x^{2})xdx
inverse oflaplace 8/((s^2+6s+8))	inverselaplace\:\frac{8}{(s^{2}+6s+8)}
derivative of log_{10}((arcsin(x)^2))	\frac{d}{dx}(\log_{10}((\arcsin(x))^{2}))
integral from-1 to 1 of (x^2-2x+3)	\int\:_{-1}^{1}(x^{2}-2x+3)dx
(\partial)/(\partial x)(y^4-6xy)	\frac{\partial\:}{\partial\:x}(y^{4}-6xy)
y^'+4y=e^{3x}	y^{\prime\:}+4y=e^{3x}
limit as x approaches 0 of 1/1	\lim\:_{x\to\:0}(\frac{1}{1})
integral of (x^2+6)sin(2x)	\int\:(x^{2}+6)\sin(2x)dx
maclaurin ln(e+x)	maclaurin\:\ln(e+x)
integral from 0 to 0.5 of x(4-8x)	\int\:_{0}^{0.5}x(4-8x)dx
integral of xcos(nx)	\int\:x\cos(nx)dx
taylor sqrt(1-2x^2)	taylor\:\sqrt{1-2x^{2}}
limit as x approaches 4 of x-5	\lim\:_{x\to\:4}(x-5)
derivative of (x^2+5/(e^x))	\frac{d}{dx}(\frac{x^{2}+5}{e^{x}})
inverse oflaplace (s+3)/(s^2+4s+4)	inverselaplace\:\frac{s+3}{s^{2}+4s+4}
maclaurin 1/(1+2x^3)	maclaurin\:\frac{1}{1+2x^{3}}
integral of sec^{14}(x)tan(x)	\int\:\sec^{14}(x)\tan(x)dx
derivative of (12/(x^5))	\frac{d}{dx}(\frac{12}{x^{5}})
integral of sin(t)	\int\:\sin(t)dt
(dy)/(dt)=y(8-y)	\frac{dy}{dt}=y(8-y)
integral of 1/((x+2))	\int\:\frac{1}{(x+2)}dx
slope of (1,-2),(-5,0)	slope\:(1,-2),(-5,0)
integral of 1/(cos^2(x+1))	\int\:\frac{1}{\cos^{2}(x+1)}dx
integral of xln(1+x)	\int\:x\ln(1+x)dx
integral from 0 to 4 of (4sqrt(x))-(2x)	\int\:_{0}^{4}(4\sqrt{x})-(2x)dx
derivative of 2x^2+5x	derivative\:2x^{2}+5x
limit as x approaches 0 of x^3sin(1/x)	\lim\:_{x\to\:0}(x^{3}\sin(\frac{1}{x}))
derivative of f(x)=2sec(x)	derivative\:f(x)=2\sec(x)

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