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Popular Calculus Problems

(dy)/(dx)=85yx^{16}	\frac{dy}{dx}=85yx^{16}
(dy)/(dt)=-5y	\frac{dy}{dt}=-5y
sum from n=0 to infinity of 2*(2/5)^n	\sum\:_{n=0}^{\infty\:}2\cdot\:(\frac{2}{5})^{n}
derivative of tan(x^5)	derivative\:\tan(x^{5})
integral of (5/(t^2)-8t^6)	\int\:(\frac{5}{t^{2}}-8t^{6})dt
integral from 0 to 1 of x^e+e^x	\int\:_{0}^{1}x^{e}+e^{x}dx
derivative of y=x5^{x+4}	derivative\:y=x5^{x+4}
integral from 0 to 2pi of e^{it}	\int\:_{0}^{2π}e^{it}dt
limit as x approaches 0 of (x_{-1})/x	\lim\:_{x\to\:0}(\frac{x_{-1}}{x})
derivative of 6sin^2(t)	derivative\:6\sin^{2}(t)
derivative of f(x)=sin(x)tan(x)	derivative\:f(x)=\sin(x)\tan(x)
integral of sin^4(1/2)x	\int\:\sin^{4}(\frac{1}{2})xdx
integral of (3x+15)sqrt(x^2+10x+4)	\int\:(3x+15)\sqrt{x^{2}+10x+4}dx
integral of (e^{2t})	\int\:(e^{2t})dt
derivative of (sin(3x))/(tan(4x))	derivative\:\frac{\sin(3x)}{\tan(4x)}
taylor 1/(x-1),21	taylor\:\frac{1}{x-1},21
derivative of f(x)=e^x(tan(x)-x)	derivative\:f(x)=e^{x}(\tan(x)-x)
integral from 0 to 1/6 of 3/(sqrt(1-9x^2))	\int\:_{0}^{\frac{1}{6}}\frac{3}{\sqrt{1-9x^{2}}}dx
(dx)/(dt)=xt	\frac{dx}{dt}=xt
y^{''}-2y^'+1y=0,y(0)=8,y^'(0)=2	y^{\prime\:\prime\:}-2y^{\prime\:}+1y=0,y(0)=8,y^{\prime\:}(0)=2
(\partial)/(\partial y)(-2e^xcos(yz))	\frac{\partial\:}{\partial\:y}(-2e^{x}\cos(yz))
integral of (1/(sqrt(2x)))	\int\:(\frac{1}{\sqrt{2x}})dx
derivative of F(x^4)	\frac{d}{dx}(F(x^{4}))
derivative of f(x)=2x^2-x+1	derivative\:f(x)=2x^{2}-x+1
integral of-8x^2	\int\:-8x^{2}dx
inverse oflaplace (e^{-pi(s)})/(s^3+s)	inverselaplace\:\frac{e^{-π(s)}}{s^{3}+s}
derivative of (x+1/x ^5)	\frac{d}{dx}((x+\frac{1}{x})^{5})
derivative of (sqrt(x)^x)	\frac{d}{dx}((\sqrt{x})^{x})
integral from 0 to infinity of ue^{-u^2}	\int\:_{0}^{\infty\:}ue^{-u^{2}}du
inverse oflaplace s/(s^2+10s+9.8)	inverselaplace\:\frac{s}{s^{2}+10s+9.8}
(dy)/(dx)=2*y/x+(y/x)^2	\frac{dy}{dx}=2\cdot\:\frac{y}{x}+(\frac{y}{x})^{2}
limit as x approaches 1+of (ln(x))/(x-1)	\lim\:_{x\to\:1+}(\frac{\ln(x)}{x-1})
limit as x approaches 0 of 6/(x^2+x)-6/x	\lim\:_{x\to\:0}(\frac{6}{x^{2}+x}-\frac{6}{x})
integral from-1 to 3 of x(x-1)(x+2)	\int\:_{-1}^{3}x(x-1)(x+2)dx
integral of x^3sqrt(x^2+19)	\int\:x^{3}\sqrt{x^{2}+19}dx
tangent of y= 4/(5x+1),(-1,-1)	tangent\:y=\frac{4}{5x+1},(-1,-1)
derivative of 9/(x^2)-3/x	derivative\:\frac{9}{x^{2}}-\frac{3}{x}
derivative of-x^3+3x+2	\frac{d}{dx}(-x^{3}+3x+2)
integral from-infinity to 6 of 1/(x^2+1)	\int\:_{-\infty\:}^{6}\frac{1}{x^{2}+1}dx
derivative of 2e^{-x^3}	\frac{d}{dx}(2e^{-x^{3}})
integral of-1/(v^2)	\int\:-\frac{1}{v^{2}}dv
integral from 1/2 to 1 of (x^{-3}-8)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-8)dx
(\partial)/(\partial x)(-7e^ysin(2x)+y+5xy)	\frac{\partial\:}{\partial\:x}(-7e^{y}\sin(2x)+y+5xy)
(\partial)/(\partial x)(x^{-7}y^2+xy^2+2xy)	\frac{\partial\:}{\partial\:x}(x^{-7}y^{2}+xy^{2}+2xy)
sum from n=0 to infinity of (2n)!	\sum\:_{n=0}^{\infty\:}(2n)!
limit as x approaches-2 of 9x^2	\lim\:_{x\to\:-2}(9x^{2})
limit as x approaches-3 of (x^2)/(9-x^2)	\lim\:_{x\to\:-3}(\frac{x^{2}}{9-x^{2}})
y^'+y/x =xy^2	y^{\prime\:}+\frac{y}{x}=xy^{2}
(2x-1)dx(3y+7)dy=0	(2x-1)dx(3y+7)dy=0
d/(dr(θ))(r(θ)cos(θ))	\frac{d}{dr(θ)}(r(θ)\cos(θ))
(\partial)/(\partial y)(e^{7yz})	\frac{\partial\:}{\partial\:y}(e^{7yz})
limit as x approaches 4+of (7x-1)/(x-4)	\lim\:_{x\to\:4+}(\frac{7x-1}{x-4})
y^{''}-8y^'=64t	y^{\prime\:\prime\:}-8y^{\prime\:}=64t
derivative of sqrt(3+\sqrt{7x)}	\frac{d}{dx}(\sqrt{3+\sqrt{7x}})
integral from 0 to 0 of x^2	\int\:_{0}^{0}x^{2}dx
(\partial)/(\partial x)(ln(x/(20)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{20}))
limit as x approaches 0 of x*1/x	\lim\:_{x\to\:0}(x\cdot\:\frac{1}{x})
integral of x/((1+x)^4)	\int\:\frac{x}{(1+x)^{4}}dx
integral of sqrt(x)(x^4+1/(x^2))	\int\:\sqrt{x}(x^{4}+\frac{1}{x^{2}})dx
integral of (t^2+t)e^{t^3+3t}	\int\:(t^{2}+t)e^{t^{3}+3t}dx
y^'+3y=2	y^{\prime\:}+3y=2
integral from 1 to 2 of (2/(x^3))	\int\:_{1}^{2}(\frac{2}{x^{3}})dx
derivative of f(x)=ln(x^3-1)	derivative\:f(x)=\ln(x^{3}-1)
area xsqrt(64-x^2),0	area\:x\sqrt{64-x^{2}},0
integral of-cos(x/2)	\int\:-\cos(\frac{x}{2})dx
derivative of sqrt(x)+7/(sqrt(x))	\frac{d}{dx}(\sqrt{x}+\frac{7}{\sqrt{x}})
derivative of (x-2pi^2)	\frac{d}{dx}((x-2π)^{2})
integral of 1/((x-1)sqrt(x^2-2x-3))	\int\:\frac{1}{(x-1)\sqrt{x^{2}-2x-3}}dx
derivative of (4x/(3x+1))	\frac{d}{dx}(\frac{4x}{3x+1})
limit as x approaches 5 of (3+1/x)^3	\lim\:_{x\to\:5}((3+\frac{1}{x})^{3})
y^'=(4x)/(e^x)	y^{\prime\:}=\frac{4x}{e^{x}}
derivative of x^2(1-9x)	derivative\:x^{2}(1-9x)
derivative of f(x)=x^4-20x^2+64	derivative\:f(x)=x^{4}-20x^{2}+64
derivative of ln((sin(x)/(cos(x))))	\frac{d}{dx}(\ln(\frac{\sin(x)}{\cos(x)}))
f(x)=sqrt(2-x^2)	f(x)=\sqrt{2-x^{2}}
integral of (sin(x))/(e^{2x)}	\int\:\frac{\sin(x)}{e^{2x}}dx
y^'=(x-1)/(y-1)	y^{\prime\:}=\frac{x-1}{y-1}
d/(dy)(-x/(y^2))	\frac{d}{dy}(-\frac{x}{y^{2}})
inverse oflaplace (-3)/((s-3)^2+4)	inverselaplace\:\frac{-3}{(s-3)^{2}+4}
integral of (72x)/((x-7)^{10)}	\int\:\frac{72x}{(x-7)^{10}}dx
integral from 0 to infinity of 1/(1+x^2)	\int\:_{0}^{\infty\:}\frac{1}{1+x^{2}}dx
area 9cos(pix),12x^2-3,-0.5,0.5	area\:9\cos(πx),12x^{2}-3,-0.5,0.5
limit as x approaches 0 of (4x)/(tan(x))	\lim\:_{x\to\:0}(\frac{4x}{\tan(x)})
integral of [(100)/(25+(5y)^2)+e^4]	\int\:[\frac{100}{25+(5y)^{2}}+e^{4}]dy
y^'=e^{2x}+3y	y^{\prime\:}=e^{2x}+3y
integral of 1/(sqrt(x^2+a^2))	\int\:\frac{1}{\sqrt{x^{2}+a^{2}}}dx
tangent of f(x)=5x-x^2,\at x=1	tangent\:f(x)=5x-x^{2},\at\:x=1
y^'=2(1+x)(1+y^2),y(0)=0	y^{\prime\:}=2(1+x)(1+y^{2}),y(0)=0
integral of (x^2+3x-1)*e^{2x}	\int\:(x^{2}+3x-1)\cdot\:e^{2x}dx
(\partial)/(\partial x)(5x^{2y})	\frac{\partial\:}{\partial\:x}(5x^{2y})
derivative of ln(csc(x-cot(x)))	\frac{d}{dx}(\ln(\csc(x)-\cot(x)))
tangent of 1/(sqrt(x))	tangent\:\frac{1}{\sqrt{x}}
integral from-1 to 1 of 1/(x^3)	\int\:_{-1}^{1}\frac{1}{x^{3}}dx
inverse oflaplace 5/((s+1)(s^2+4s+3))	inverselaplace\:\frac{5}{(s+1)(s^{2}+4s+3)}
(dh)/(dt)=-sqrt(h)	\frac{dh}{dt}=-\sqrt{h}
integral of 2x^4	\int\:2x^{4}dx
area sqrt(x),0,4	area\:\sqrt{x},0,4
derivative of sqrt(6-5cos(2x))	derivative\:\sqrt{6-5\cos(2x)}
f(x)=xsqrt(x^2+1)	f(x)=x\sqrt{x^{2}+1}
integral of sin(9x)ln(sin(9x))	\int\:\sin(9x)\ln(\sin(9x))dx

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