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Popular Calculus Problems

y^'=9x+y,y(0)=4	y^{\prime\:}=9x+y,y(0)=4
integral from 0 to 1 of (13)/(4y-1)	\int\:_{0}^{1}\frac{13}{4y-1}dy
derivative of \sqrt[3]{x^4+5x}	derivative\:\sqrt[3]{x^{4}+5x}
derivative of e^{-8x}	derivative\:e^{-8x}
sum from n=0 to infinity of e^n	\sum\:_{n=0}^{\infty\:}e^{n}
(4x)^'	(4x)^{\prime\:}
tangent of 2sqrt(3)sin(x)+2cos(x)	tangent\:2\sqrt{3}\sin(x)+2\cos(x)
integral of 2cos(sqrt(10x))	\int\:2\cos(\sqrt{10x})dx
derivative of (x^2+sin(x)^3)	\frac{d}{dx}((x^{2}+\sin(x))^{3})
integral from-1 to 1 of x^3-x	\int\:_{-1}^{1}x^{3}-xdx
laplacetransform 1e^{4t}	laplacetransform\:1e^{4t}
integral of (x^2)/((x^3+2)^2)	\int\:\frac{x^{2}}{(x^{3}+2)^{2}}dx
tangent of (6x)/(x+7),\at x=1	tangent\:\frac{6x}{x+7},\at\:x=1
(\partial)/(\partial y)(xe^{y/x})	\frac{\partial\:}{\partial\:y}(xe^{\frac{y}{x}})
derivative of x^2-2	derivative\:x^{2}-2
integral of (y^2+6y+9)/((y^2+9)^2)	\int\:\frac{y^{2}+6y+9}{(y^{2}+9)^{2}}dy
tangent of f(x)=3sqrt(x-1),\at x=5	tangent\:f(x)=3\sqrt{x-1},\at\:x=5
sum from n=1 to infinity of (n!)/((2n)!)	\sum\:_{n=1}^{\infty\:}\frac{n!}{(2n)!}
derivative of x^4+4/3 x^3-4x^2-4/3	derivative\:x^{4}+\frac{4}{3}x^{3}-4x^{2}-\frac{4}{3}
integral of (y+1)/(y^2+1)	\int\:\frac{y+1}{y^{2}+1}dy
tangent of f(x)=5x^3-5x,(-1,0)	tangent\:f(x)=5x^{3}-5x,(-1,0)
integral of x(4x+5)^3	\int\:x(4x+5)^{3}dx
implicit (dy)/(dx),xy=28	implicit\:\frac{dy}{dx},xy=28
slope of (-1.2)(-2.3)	slope\:(-1.2)(-2.3)
integral of sin^4(y)cos(y)	\int\:\sin^{4}(y)\cos(y)dy
derivative of ln(\sqrt[4]{(6x+1/(6-x)}))	\frac{d}{dx}(\ln(\sqrt[4]{\frac{6x+1}{6-x}}))
derivative of (0.001x/(0.001x+1))	\frac{d}{dx}(\frac{0.001x}{0.001x+1})
derivative of y=x^2sin(x)	derivative\:y=x^{2}\sin(x)
(x^8)^'	(x^{8})^{\prime\:}
integral of sec^2(x)-8	\int\:\sec^{2}(x)-8dx
taylor (x-pi)^3	taylor\:(x-π)^{3}
sum from n=1 to infinity of 3n	\sum\:_{n=1}^{\infty\:}3n
integral of xcsc(x)cot(x)	\int\:x\csc(x)\cot(x)dx
integral from 0 to 8 of x+1	\int\:_{0}^{8}x+1dx
integral of sec(2x+1)tan(2x+1)	\int\:\sec(2x+1)\tan(2x+1)dx
limit as x approaches 1+of ln^{x-1}(x)	\lim\:_{x\to\:1+}(\ln^{x-1}(x))
integral of 1/(\sqrt[3]{x^4)}	\int\:\frac{1}{\sqrt[3]{x^{4}}}dx
d/(dt)(-cos^2(t))	\frac{d}{dt}(-\cos^{2}(t))
integral of (x^9)/(1+x^{20)}	\int\:\frac{x^{9}}{1+x^{20}}dx
laplacetransform 4e^{-3t+2}	laplacetransform\:4e^{-3t+2}
limit as x approaches infinity of-4/x	\lim\:_{x\to\:\infty\:}(-\frac{4}{x})
integral of (e^{sqrt(x)})/(2sqrt(x))	\int\:\frac{e^{\sqrt{x}}}{2\sqrt{x}}dx
limit as x approaches-1 of 6	\lim\:_{x\to\:-1}(6)
derivative of 8f-g,\at g(2)	derivative\:8f-g,\at\:g(2)
integral from 5 to 10 of sqrt(100-x^2)	\int\:_{5}^{10}\sqrt{100-x^{2}}dx
derivative of pi^3	\frac{d}{dx}(π^{3})
derivative of 1/8 x^2-7x+16	derivative\:\frac{1}{8}x^{2}-7x+16
(\partial)/(\partial x)(6xe^{xy})	\frac{\partial\:}{\partial\:x}(6xe^{xy})
integral of sin(x)cox	\int\:\sin(x)coxdx
integral of (5sqrt(x)+4sin(x))	\int\:(5\sqrt{x}+4\sin(x))dx
derivative of 2(13-x^4)	\frac{d}{dx}(2(13-x^{4}))
derivative of acsc^2(kx)	\frac{d}{dx}(a\csc^{2}(kx))
derivative of (6x+5(x^3-2))	\frac{d}{dx}((6x+5)(x^{3}-2))
derivative of e^{e^{e^{e^x}}}	\frac{d}{dx}(e^{e^{e^{e^{x}}}})
integral of r^2	\int\:r^{2}dr
limit as x approaches 0 of (7x)/(cot(x))	\lim\:_{x\to\:0}(\frac{7x}{\cot(x)})
(\partial)/(\partial s)(ssin(t))	\frac{\partial\:}{\partial\:s}(s\sin(t))
integral of 2sin(x)\sqrt[3]{1+cos(x)}	\int\:2\sin(x)\sqrt[3]{1+\cos(x)}dx
derivative of (x^3-2xsqrt(x)/x)	\frac{d}{dx}(\frac{x^{3}-2x\sqrt{x}}{x})
slope of (0,-9),(7,6)	slope\:(0,-9),(7,6)
tangent of f(x)=x(x^2-4x+5)^5,\at x=2	tangent\:f(x)=x(x^{2}-4x+5)^{5},\at\:x=2
xy^'=2y+e^xx^3	x\cdot\:y^{\prime\:}=2y+e^{x}\cdot\:x^{3}
limit as x approaches-1/2 of 7/(2x+1)	\lim\:_{x\to\:-\frac{1}{2}}(\frac{7}{2x+1})
area-x^2+2x,3x^3-x^2-10x	area\:-x^{2}+2x,3x^{3}-x^{2}-10x
derivative of 5sin(-3x+pi/4)	derivative\:5\sin(-3x+\frac{π}{4})
limit as x approaches 3 of 5^2-9x+7	\lim\:_{x\to\:3}(5^{2}-9x+7)
integral from-2 to 3 of x^2-3	\int\:_{-2}^{3}x^{2}-3dx
laplacetransform e^{5t}t^3	laplacetransform\:e^{5t}t^{3}
integral of x^3sqrt(x^2+1)	\int\:x^{3}\sqrt{x^{2}+1}dx
integral of (e^{3x})/(e^{3x)+2}	\int\:\frac{e^{3x}}{e^{3x}+2}dx
derivative of (x^4+3/(6x))	\frac{d}{dx}(\frac{x^{4}+3}{6x})
d/(dy)(3y)	\frac{d}{dy}(3y)
derivative of 1+2e^{3x}	\frac{d}{dx}(1+2e^{3x})
area f(y)=2sqrt(x),0,4	area\:f(y)=2\sqrt{x},0,4
derivative of arctan(sin(2x))	\frac{d}{dx}(\arctan(\sin(2x)))
integral of sqrt(1-4(1/2 sin(x))^2)	\int\:\sqrt{1-4(\frac{1}{2}\sin(x))^{2}}dx
derivative of ln(1-5x)	derivative\:\ln(1-5x)
laplacetransform f(t)=e^{2(t-2)}	laplacetransform\:f(t)=e^{2(t-2)}
derivative of f(x)=(1+x)/((2x^2+1)^2)	derivative\:f(x)=\frac{1+x}{(2x^{2}+1)^{2}}
d/(dt)(t^3-5t^2+9t)	\frac{d}{dt}(t^{3}-5t^{2}+9t)
area y=2x+2,y=x^2-2	area\:y=2x+2,y=x^{2}-2
area y^2=2x,y=-4+x	area\:y^{2}=2x,y=-4+x
integral of 1/(sqrt(25-4x^2))	\int\:\frac{1}{\sqrt{25-4x^{2}}}dx
integral of t*cos(t)	\int\:t\cdot\:\cos(t)dt
integral of 18sin^3(x)cos^2(x)	\int\:18\sin^{3}(x)\cos^{2}(x)dx
y^{''}+4y^'+5y=-10x+e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-10x+e^{-x}
laplacetransform te^{2t}sin(6t)	laplacetransform\:te^{2t}\sin(6t)
derivative of e^xcos(x-x^3sin(x)+pi)	\frac{d}{dx}(e^{x}\cos(x)-x^{3}\sin(x)+π)
y^'= y/(50)5,y(0)=30	y^{\prime\:}=\frac{y}{50}5,y(0)=30
slope of (7,6),(-7,-7)	slope\:(7,6),(-7,-7)
(dy)/(dx)= y/x+sqrt((y/x)^2-1)	\frac{dy}{dx}=\frac{y}{x}+\sqrt{(\frac{y}{x})^{2}-1}
y^{''}+3y^'+2y= 1/(1+e^t)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\frac{1}{1+e^{t}}
integral of xsqrt(1+x)+(x^2+4)/(x-1)	\int\:x\sqrt{1+x}+\frac{x^{2}+4}{x-1}dx
derivative of x^3ln(x^4+1)	\frac{d}{dx}(x^{3}\ln(x^{4}+1))
integral from 2 to x^2 of cos(t^2+1)	\int\:_{2}^{x^{2}}\cos(t^{2}+1)dt
derivative of y=xcos(x)	derivative\:y=x\cos(x)
area x=63-7y^2,x=7y^2-63	area\:x=63-7y^{2},x=7y^{2}-63
derivative of t^3-t	derivative\:t^{3}-t
derivative of sqrt(1-x^2)-xarccos(x)	\frac{d}{dx}(\sqrt{1-x^{2}}-x\arccos(x))
y(dy)/(dx)=-8cos(pix)	y\frac{dy}{dx}=-8\cos(πx)

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