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Popular Calculus Problems

integral from-3 to-5 of (-5)^{-3}	\int\:_{-3}^{-5}(-5)^{-3}dx
derivative of-(y^2/((x-y)^2))	\frac{d}{dx}(-\frac{y^{2}}{(x-y)^{2}})
derivative of 2^{x^2}	derivative\:2^{x^{2}}
integral of 1/((x^2+2)^{3/2)}	\int\:\frac{1}{(x^{2}+2)^{\frac{3}{2}}}dx
integral of 1/(x^2+8x+25)	\int\:\frac{1}{x^{2}+8x+25}dx
xy^'+(1-x)y=2xe^x	xy^{\prime\:}+(1-x)y=2xe^{x}
limit as x approaches 4-of 5/(x-4)	\lim\:_{x\to\:4-}(\frac{5}{x-4})
integral of (2x)/(sqrt(1-4x^2))	\int\:\frac{2x}{\sqrt{1-4x^{2}}}dx
(\partial)/(\partial y)(x^3y-3xy^2)	\frac{\partial\:}{\partial\:y}(x^{3}y-3xy^{2})
integral from 0 to 7 of 1/(sqrt(49+t^2))	\int\:_{0}^{7}\frac{1}{\sqrt{49+t^{2}}}dt
derivative of e^{ax}	\frac{d}{dx}(e^{ax})
derivative of 4+sqrt(1-x)	\frac{d}{dx}(4+\sqrt{1-x})
integral from 0 to 1 of 9e^{x^2}	\int\:_{0}^{1}9e^{x^{2}}dx
t^2y^'+y^'=ty	t^{2}y^{\prime\:}+y^{\prime\:}=ty
derivative of cos(sqrt(sin(cot(pix))))	derivative\:\cos(\sqrt{\sin(\cot(πx))})
tangent of 2x+3/x	tangent\:2x+\frac{3}{x}
integral from 0 to 4 of \|x-3\|	\int\:_{0}^{4}\left\|x-3\right\|dx
derivative of f(x)=(4x^2+4x+6)/(sqrt(x))	derivative\:f(x)=\frac{4x^{2}+4x+6}{\sqrt{x}}
integral of (x^3+x^2+x+3)/(x^4+4x^2+3)	\int\:\frac{x^{3}+x^{2}+x+3}{x^{4}+4x^{2}+3}dx
derivative of (x^2+8^5)	\frac{d}{dx}((x^{2}+8)^{5})
integral of (1-x)(2+x^3)	\int\:(1-x)(2+x^{3})dx
derivative of (x^2+6)/(5x-2)	derivative\:\frac{x^{2}+6}{5x-2}
integral of e^{(y^2)}	\int\:e^{(y^{2})}dy
integral from 0 to 1 of (x-sqrt(x))	\int\:_{0}^{1}(x-\sqrt{x})dx
(\partial)/(\partial x)(y-1/(x^2))	\frac{\partial\:}{\partial\:x}(y-\frac{1}{x^{2}})
derivative of e^{(1/t ln((5^t+13^t)/2))}	derivative\:e^{(\frac{1}{t}\ln(\frac{5^{t}+13^{t}}{2}))}
(dy)/(dt)+50y=0	\frac{dy}{dt}+50y=0
area 9x^2ln(x),36ln(x)	area\:9x^{2}\ln(x),36\ln(x)
integral of 9/32+9/8 x^2	\int\:\frac{9}{32}+\frac{9}{8}x^{2}dx
integral of 6/((t^2+1)^{3/2)}	\int\:\frac{6}{(t^{2}+1)^{\frac{3}{2}}}dt
(\partial)/(\partial v)(2u)	\frac{\partial\:}{\partial\:v}(2u)
(\partial)/(\partial x)(20-5xy-5x)	\frac{\partial\:}{\partial\:x}(20-5xy-5x)
limit as x approaches 2+of x-3	\lim\:_{x\to\:2+}(x-3)
integral from 1 to 2 of 2/(x^2)	\int\:_{1}^{2}\frac{2}{x^{2}}dx
derivative of (3x-x^2/(sqrt(x))-4cot(x))	\frac{d}{dx}(\frac{3x-x^{2}}{\sqrt{x}}-4\cot(x))
derivative of f(x)=3cos(cos(x^6))	derivative\:f(x)=3\cos(\cos(x^{6}))
integral from-infinity to 0 of 1/(2-10x)	\int\:_{-\infty\:}^{0}\frac{1}{2-10x}dx
(x^2sin(x)+4y)dx+xdy=0	(x^{2}\sin(x)+4y)dx+xdy=0
derivative of 3^{sqrt(x^2-1)}	\frac{d}{dx}(3^{\sqrt{x^{2}-1}})
derivative of at^5-5bt^3	\frac{d}{dx}(at^{5}-5bt^{3})
limit as x approaches-2-of sqrt(2x+4)-2	\lim\:_{x\to\:-2-}(\sqrt{2x+4}-2)
integral of cos(2x)tan(2x)	\int\:\cos(2x)\tan(2x)dx
limit as z approaches 1 of (z+2)/(z^4-1)	\lim\:_{z\to\:1}(\frac{z+2}{z^{4}-1})
derivative of f(x)=(x-2)^2(x+3)^3	derivative\:f(x)=(x-2)^{2}(x+3)^{3}
integral of xarcsin(x^2)	\int\:x\arcsin(x^{2})dx
integral of (x^2)/((100+x^2)^2)	\int\:\frac{x^{2}}{(100+x^{2})^{2}}dx
integral from 10 to 19 of ln(x^{15})	\int\:_{10}^{19}\ln(x^{15})dx
tangent of f(x)=(1-x)(x^2-6)^2,\at x=3	tangent\:f(x)=(1-x)(x^{2}-6)^{2},\at\:x=3
integral of 1+xe^{-x}	\int\:1+xe^{-x}dx
integral of tan^7(x)sec^7(x)	\int\:\tan^{7}(x)\sec^{7}(x)dx
integral of log_{5}(x)	\int\:\log_{5}(x)dx
integral of \|4x+1\|	\int\:\left\|4x+1\right\|dx
integral of sin(e^t)	\int\:\sin(e^{t})dt
(\partial)/(\partial x)((4x^2y^2)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{4x^{2}y^{2}}{x+y})
derivative of f(x)=x^2-6x+5	derivative\:f(x)=x^{2}-6x+5
integral from-4 to 3 of \| 1/2 x\|	\int\:_{-4}^{3}\left\|\frac{1}{2}x\right\|dx
derivative of t/(1+t^2)	derivative\:\frac{t}{1+t^{2}}
tangent of f(x)=(8x)/(x^2+1),(0,0)	tangent\:f(x)=\frac{8x}{x^{2}+1},(0,0)
integral of 2/(sec(2x)-1)	\int\:\frac{2}{\sec(2x)-1}dx
integral of sec^2(5θ)	\int\:\sec^{2}(5θ)dθ
(\partial)/(\partial x)((x+2)/(y-2)+1/x)	\frac{\partial\:}{\partial\:x}(\frac{x+2}{y-2}+\frac{1}{x})
integral of (4-3cos(x))/(sin^2(x))	\int\:\frac{4-3\cos(x)}{\sin^{2}(x)}dx
limit as x approaches 0 of (8e^{2x}-8e^{-4x}-36x-6)/(3x^2+4x)	\lim\:_{x\to\:0}(\frac{8e^{2x}-8e^{-4x}-36x-6}{3x^{2}+4x})
integral of-x^n	\int\:-x^{n}dx
slope of x^2-8x-5	slope\:x^{2}-8x-5
integral of (x+3)/(x^2+16)	\int\:\frac{x+3}{x^{2}+16}dx
limit as t approaches 8 of (t(t-5)-24)/(t^2-8t)	\lim\:_{t\to\:8}(\frac{t(t-5)-24}{t^{2}-8t})
limit as z approaches 2i of (1-z)/(1+z)	\lim\:_{z\to\:2i}(\frac{1-z}{1+z})
sum from n=1 to infinity of 3r^n	\sum\:_{n=1}^{\infty\:}3r^{n}
limit as x approaches 3-of 2x+5	\lim\:_{x\to\:3-}(2x+5)
limit as x approaches infinity of 4x+14	\lim\:_{x\to\:\infty\:}(4x+14)
derivative of ln(x+c)	\frac{d}{dx}(\ln(x)+c)
(\partial)/(\partial x)(54-2/3 x^2-4y^2)	\frac{\partial\:}{\partial\:x}(54-\frac{2}{3}x^{2}-4y^{2})
integral of 3/(sqrt(1-x^2))	\int\:\frac{3}{\sqrt{1-x^{2}}}dx
integral from 0 to ln(3) of 4/(e^x+2)	\int\:_{0}^{\ln(3)}\frac{4}{e^{x}+2}dx
limit as t approaches 0 of 4/t-4/(e^t-1)	\lim\:_{t\to\:0}(\frac{4}{t}-\frac{4}{e^{t}-1})
limit as x approaches 4 of sqrt(2x-1)	\lim\:_{x\to\:4}(\sqrt{2x-1})
derivative of 5e^{4x}	\frac{d}{dx}(5e^{4x})
integral of (sin^5(sqrt(x)))/(sqrt(x))	\int\:\frac{\sin^{5}(\sqrt{x})}{\sqrt{x}}dx
integral of x^2\sqrt[3]{7x^3+1}	\int\:x^{2}\sqrt[3]{7x^{3}+1}dx
limit as x approaches-infinity of 4e^{-x}	\lim\:_{x\to\:-\infty\:}(4e^{-x})
dy-(y-3)^2dx=0	dy-(y-3)^{2}dx=0
integral of x^2cos(x)	\int\:x^{2}\cos(x)dx
derivative of f(x)=(x^{2/3})/(x^{1/3)+2}	derivative\:f(x)=\frac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}+2}
derivative of (tan(x-5)/(sec(x)))	\frac{d}{dx}(\frac{\tan(x)-5}{\sec(x)})
(dx)/(dy)=(x-11)/(3y+2513),y(0)=77	\frac{dx}{dy}=\frac{x-11}{3y+2513},y(0)=77
limit as t approaches 2 of 3-sqrt(t+7)	\lim\:_{t\to\:2}(3-\sqrt{t+7})
f(x)=(sin(x))/(1-cos(x))	f(x)=\frac{\sin(x)}{1-\cos(x)}
derivative of 5/(1+x^2)	derivative\:\frac{5}{1+x^{2}}
area x=2sqrt(3y),x=0,y=7	area\:x=2\sqrt{3y},x=0,y=7
inverse oflaplace ((2s+1))/(s^2+2s+2)	inverselaplace\:\frac{(2s+1)}{s^{2}+2s+2}
integral of-5sec^2(x)	\int\:-5\sec^{2}(x)dx
tangent of f(x)=x^3-25x+5,\at x=5	tangent\:f(x)=x^{3}-25x+5,\at\:x=5
y^'=((x^2-y^2))/(xy),y(2)=4	y^{\prime\:}=\frac{(x^{2}-y^{2})}{xy},y(2)=4
integral of e^{6u}	\int\:e^{6u}du
tangent of f(x)=(x-9)/(8x-1),\at x=1	tangent\:f(x)=\frac{x-9}{8x-1},\at\:x=1
derivative of log_{3}(x)	derivative\:\log_{3}(x)
y^{'''}+6y^{''}-15y^'+8y=0	y^{\prime\:\prime\:\prime\:}+6y^{\prime\:\prime\:}-15y^{\prime\:}+8y=0
derivative of (x^2/(9+4x))	\frac{d}{dx}(\frac{x^{2}}{9+4x})
integral from 1/7 to 5 of 8xln(7x)	\int\:_{\frac{1}{7}}^{5}8x\ln(7x)dx

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