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Popular Calculus Problems

integral from-1 to 1 of (1-x)	\int\:_{-1}^{1}(1-x)dx
integral of (x-1)/(x^2+9)	\int\:\frac{x-1}{x^{2}+9}dx
y^{''}+4y^'+5y=8	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=8
tangent of-5x^2+4	tangent\:-5x^{2}+4
derivative of 6-5cos((pix/(15)))	\frac{d}{dx}(6-5\cos(\frac{πx}{15}))
integral of (x^4+4)/(x^4)	\int\:\frac{x^{4}+4}{x^{4}}dx
derivative of sqrt(x-1)+sqrt(x+1)	\frac{d}{dx}(\sqrt{x-1}+\sqrt{x+1})
integral of 200sin(5x)\sqrt[3]{cos(5x)}	\int\:200\sin(5x)\sqrt[3]{\cos(5x)}dx
limit as b approaches 7 of 6b+31	\lim\:_{b\to\:7}(6b+31)
integral from 0 to 1 of (x^2+5x)e^{-x}	\int\:_{0}^{1}(x^{2}+5x)e^{-x}dx
integral from 0 to 5 of x^{3/2}	\int\:_{0}^{5}x^{\frac{3}{2}}dx
integral of (4x^2+x+17)/((x^2+5)(x-3))	\int\:\frac{4x^{2}+x+17}{(x^{2}+5)(x-3)}dx
integral of 1-ln(x)	\int\:1-\ln(x)dx
integral of x^7sqrt(x^4+6)	\int\:x^{7}\sqrt{x^{4}+6}dx
derivative of (x^3-sec(3x^2-4))^{-3}	derivative\:(x^{3}-\sec(3x^{2}-4))^{-3}
derivative of 2/(sqrt(x)-1)	\frac{d}{dx}(\frac{2}{\sqrt{x}}-1)
y^{''}+3y^'+2y=0,y(1)=1,y^'(1)=0	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=0,y(1)=1,y^{\prime\:}(1)=0
derivative of-8/(x^2)-8/(x^3)	derivative\:-\frac{8}{x^{2}}-\frac{8}{x^{3}}
integral of (x^2+x)/(x^4-3x^2-4)	\int\:\frac{x^{2}+x}{x^{4}-3x^{2}-4}dx
derivative of 1/(sqrt(5-6x))	\frac{d}{dx}(\frac{1}{\sqrt{5-6x}})
limit as x approaches 0 of (sin(x/5))/x	\lim\:_{x\to\:0}(\frac{\sin(\frac{x}{5})}{x})
(dy)/(dx)=(2x(y-2))/(x^2+1),y(0)=4	\frac{dy}{dx}=\frac{2x(y-2)}{x^{2}+1},y(0)=4
y^{''''}-81y=0	y^{\prime\:\prime\:\prime\:\prime\:}-81y=0
(\partial)/(\partial x)(-e^{-x})	\frac{\partial\:}{\partial\:x}(-e^{-x})
derivative of (x^2-9x+8)/(x^2+9)	derivative\:\frac{x^{2}-9x+8}{x^{2}+9}
sum from n=1 to infinity of 8/n-8/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{8}{n}-\frac{8}{n+1}
integral of (6x-11)/((x-1)^2)	\int\:\frac{6x-11}{(x-1)^{2}}dx
derivative of 6/((6-x^6)^{3/2)}	derivative\:\frac{6}{(6-x^{6})^{\frac{3}{2}}}
integral of (x^3)/((x^2+4)^{3/2)}	\int\:\frac{x^{3}}{(x^{2}+4)^{\frac{3}{2}}}dx
derivative of 6/((s+3)^2)	derivative\:\frac{6}{(s+3)^{2}}
integral of (1-3x)^{1/2}	\int\:(1-3x)^{\frac{1}{2}}dx
laplacetransform x^2	laplacetransform\:x^{2}
inverse oflaplace (2s+1)/(s^2)	inverselaplace\:\frac{2s+1}{s^{2}}
xy^'+y=xy^3	xy^{\prime\:}+y=xy^{3}
sum from n=0 to infinity of (3/8)^{n/2}	\sum\:_{n=0}^{\infty\:}(\frac{3}{8})^{\frac{n}{2}}
(dv)/(dx)=x	\frac{dv}{dx}=x
y^{'''}+y^{''}=0	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}=0
(dy)/(dx)= x/(y-2)	\frac{dy}{dx}=\frac{x}{y-2}
10^{-3}y^'+10y=220cos(50t)	10^{-3}y^{\prime\:}+10y=220\cos(50t)
integral from 0 to 4 of 2pix(1/(x+3))	\int\:_{0}^{4}2πx(\frac{1}{x+3})dx
limit as x approaches 3 of x^2-3x+4	\lim\:_{x\to\:3}(x^{2}-3x+4)
integral of 1/(sqrt(12+4x-x^2))	\int\:\frac{1}{\sqrt{12+4x-x^{2}}}dx
integral of 3sin(2/3 x)	\int\:3\sin(\frac{2}{3}x)dx
integral of csc(ay)cot(ay)	\int\:\csc(ay)\cot(ay)dy
derivative of sqrt(x+1)-x^2+x	\frac{d}{dx}(\sqrt{x+1}-x^{2}+x)
integral of sin(log_{10}(x))	\int\:\sin(\log_{10}(x))dx
derivative of (x^2-1)/((2x-5)^2)	derivative\:\frac{x^{2}-1}{(2x-5)^{2}}
(\partial)/(\partial x)(ln(sqrt(1-2x)))	\frac{\partial\:}{\partial\:x}(\ln(\sqrt{1-2x}))
derivative of 4cos(sin(3x))	\frac{d}{dx}(4\cos(\sin(3x)))
y^{'''}+y^'=t^2	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=t^{2}
(\partial)/(\partial x)(x^{1/3}y^3)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{3}}y^{3})
integral of (5x-4)/(2x^2+x-1)	\int\:\frac{5x-4}{2x^{2}+x-1}dx
limit as t approaches 0 of (sin(4t))/t	\lim\:_{t\to\:0}(\frac{\sin(4t)}{t})
derivative of 65x^{9/10}	derivative\:65x^{\frac{9}{10}}
y^'+2y=5sin(e^{2x})	y^{\prime\:}+2y=5\sin(e^{2x})
integral of xcos(x/3)	\int\:x\cos(\frac{x}{3})dx
integral of cos(x)csc^6(x)	\int\:\cos(x)\csc^{6}(x)dx
integral of 1/(3+y)	\int\:\frac{1}{3+y}dy
integral from 0 to 1 of 1/(1+9x^2)	\int\:_{0}^{1}\frac{1}{1+9x^{2}}dx
(\partial)/(\partial x)(2x-4)	\frac{\partial\:}{\partial\:x}(2x-4)
(\partial)/(\partial y)(-sin(xy))	\frac{\partial\:}{\partial\:y}(-\sin(xy))
(dP)/(dt)=0.2P-0.001P^2	\frac{dP}{dt}=0.2P-0.001P^{2}
derivative of-(2e^x/(x^3)+(e^x)/(x^2))	\frac{d}{dx}(-\frac{2e^{x}}{x^{3}}+\frac{e^{x}}{x^{2}})
(\partial)/(\partial x)(30y^7x^4-20y^6x^3)	\frac{\partial\:}{\partial\:x}(30y^{7}x^{4}-20y^{6}x^{3})
derivative of-30x^3+(12x/5-1/3)	\frac{d}{dx}(-30x^{3}+\frac{12x}{5}-\frac{1}{3})
(2e^{3x})^'	(2e^{3x})^{\prime\:}
derivative of sin(xcos(2x))	\frac{d}{dx}(\sin(x)\cos(2x))
(\partial)/(\partial x)(3x^2+2y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}+2y^{2})
integral from z-1 to 1 of 3x^2-4zx+2z^2	\int\:_{z-1}^{1}3x^{2}-4zx+2z^{2}
derivative of ln(3x^2+4)	\frac{d}{dx}(\ln(3x^{2}+4))
limit as x approaches-5 of (x^2-8)/(5-x)	\lim\:_{x\to\:-5}(\frac{x^{2}-8}{5-x})
derivative of 24x^{3/2}	\frac{d}{dx}(24x^{\frac{3}{2}})
(dy)/(dx)=5x(x-3)	\frac{dy}{dx}=5x(x-3)
y^'-y=7te^{2t},y(0)=1	y^{\prime\:}-y=7te^{2t},y(0)=1
maclaurin e^x-1	maclaurin\:e^{x}-1
derivative of (1-sqrt(x)/(1+sqrt(x)))	\frac{d}{dx}(\frac{1-\sqrt{x}}{1+\sqrt{x}})
integral of (4x-6)/(x^2+4)	\int\:\frac{4x-6}{x^{2}+4}dx
integral of 3/2 x^2	\int\:\frac{3}{2}x^{2}dx
integral of 1/(x^3-2x^2+x)	\int\:\frac{1}{x^{3}-2x^{2}+x}dx
(\partial)/(\partial y)(2z)	\frac{\partial\:}{\partial\:y}(2z)
simplify (2x)/(sqrt(x^2+1))	simplify\:\frac{2x}{\sqrt{x^{2}+1}}
integral of (4+6x-3x^2)/(sqrt(x))	\int\:\frac{4+6x-3x^{2}}{\sqrt{x}}dx
integral of (8+x^4)^34x^3	\int\:(8+x^{4})^{3}4x^{3}dx
integral of sqrt(x)-2/(\sqrt[3]{x)}	\int\:\sqrt{x}-\frac{2}{\sqrt[3]{x}}dx
(dy)/(dt)=0.2y(1000-y)	\frac{dy}{dt}=0.2y(1000-y)
f(x)=xsqrt(2)	f(x)=x\sqrt{2}
(\partial)/(\partial x)(5x)	\frac{\partial\:}{\partial\:x}(5x)
area 2sin(x),6cos(x),[0,pi]	area\:2\sin(x),6\cos(x),[0,π]
integral of ((ln(z))^6)/z	\int\:\frac{(\ln(z))^{6}}{z}dz
integral of 1/((a+b)+(a-b)x^2)	\int\:\frac{1}{(a+b)+(a-b)x^{2}}dx
integral of x/(sqrt(x-8))	\int\:\frac{x}{\sqrt{x-8}}dx
integral from 0 to 1 of 2xarctan(x^2)	\int\:_{0}^{1}2x\arctan(x^{2})dx
(dy)/(dx)=4x^5y-y	\frac{dy}{dx}=4x^{5}y-y
integral from-2 to 0 of (y/2+sqrt(y+3))	\int\:_{-2}^{0}(\frac{y}{2}+\sqrt{y+3})dy
laplacetransform e^{-2t}sin(5t)	laplacetransform\:e^{-2t}\sin(5t)
derivative of 6e^{x^{-5}}	derivative\:6e^{x^{-5}}
tangent of f(x)= 1/(3+2x),(1, 1/5)	tangent\:f(x)=\frac{1}{3+2x},(1,\frac{1}{5})
derivative of (cx+b/(4x+d))	\frac{d}{dx}(\frac{cx+b}{4x+d})
(d^2)/(dx^2)(cos(x^2))	\frac{d^{2}}{dx^{2}}(\cos(x^{2}))
integral of-x^5sin(x)	\int\:-x^{5}\sin(x)dx

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