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Popular Calculus Problems

derivative of y= 1/(3x^2)-5/(2x)	derivative\:y=\frac{1}{3x^{2}}-\frac{5}{2x}
integral of 3/2 t^2	\int\:\frac{3}{2}t^{2}dt
tangent of f(x)=-3x^2-2,\at x=5	tangent\:f(x)=-3x^{2}-2,\at\:x=5
integral of-4xe^{x^2}	\int\:-4xe^{x^{2}}dx
integral of xsec^2(2x)	\int\:x\sec^{2}(2x)dx
inverse oflaplace 3/((s-1)^2)	inverselaplace\:\frac{3}{(s-1)^{2}}
integral of (48x^2)/((x-15)(x+5)^2)	\int\:\frac{48x^{2}}{(x-15)(x+5)^{2}}dx
limit as x approaches-3 of 4x^2+3x+2	\lim\:_{x\to\:-3}(4x^{2}+3x+2)
(1-x^2)(dy)/(dx)=xy+y	(1-x^{2})\frac{dy}{dx}=xy+y
derivative of y=(2x+1)/x	derivative\:y=\frac{2x+1}{x}
d/(dt)(-6t)	\frac{d}{dt}(-6t)
inverse oflaplace (2x)/(x^2+2x)+x+5	inverselaplace\:\frac{2x}{x^{2}+2x}+x+5
limit as x approaches 1 of x^{1/(x-1)}	\lim\:_{x\to\:1}(x^{\frac{1}{x-1}})
derivative of 1/((1+x))	\frac{d}{dx}(\frac{1}{(1+x)})
derivative of (1+2x)e^{3x^2}	derivative\:(1+2x)e^{3x^{2}}
derivative of \sqrt[3]{5x^3-pix+1}	\frac{d}{dx}(\sqrt[3]{5x^{3}-πx+1})
y^{''}-14y^'+48y=0	y^{\prime\:\prime\:}-14y^{\prime\:}+48y=0
inverse oflaplace 3/(s*(s+2))	inverselaplace\:\frac{3}{s\cdot\:(s+2)}
area 8x^2-5x,x^3-8x+3	area\:8x^{2}-5x,x^{3}-8x+3
integral of sqrt(x+10)	\int\:\sqrt{x+10}dx
(e^xcos(x))^'	(e^{x}\cos(x))^{\prime\:}
integral from 0 to pi/2 of cos(5t)cos(10t)	\int\:_{0}^{\frac{π}{2}}\cos(5t)\cos(10t)dt
integral of (x^3)/4	\int\:\frac{x^{3}}{4}dx
xy^'-2y= 3/(2x)	xy^{\prime\:}-2y=\frac{3}{2x}
(d^2)/(dx^2)(sin(3x^2+2))	\frac{d^{2}}{dx^{2}}(\sin(3x^{2}+2))
integral of sin^3(x)cos^6(x)	\int\:\sin^{3}(x)\cos^{6}(x)dx
integral of 6x^{3/2}-3x^{-3/2}	\int\:6x^{\frac{3}{2}}-3x^{-\frac{3}{2}}dx
limit as x approaches 0 of cos(x)-1	\lim\:_{x\to\:0}(\cos(x)-1)
derivative of (sqrt(3))/(x^5)	derivative\:\frac{\sqrt{3}}{x^{5}}
integral of x^3sqrt(2+x^2)	\int\:x^{3}\sqrt{2+x^{2}}dx
integral of (5x+3)(x^2-9)	\int\:(5x+3)(x^{2}-9)dx
derivative of x^2+y^2+xy	\frac{d}{dx}(x^{2}+y^{2}+xy)
area y=2x-2x^2,[0,1]	area\:y=2x-2x^{2},[0,1]
area y= 1/(x^2),y=0,x=1,x=5	area\:y=\frac{1}{x^{2}},y=0,x=1,x=5
limit as x approaches 0 of (sin(2x))/x+4	\lim\:_{x\to\:0}(\frac{\sin(2x)}{x}+4)
derivative of (2x^2-4x^{1/2})	\frac{d}{dx}((2x^{2}-4x)^{\frac{1}{2}})
limit as x approaches infinity of x^2+3	\lim\:_{x\to\:\infty\:}(x^{2}+3)
integral from 0 to 12 of sqrt(3x)	\int\:_{0}^{12}\sqrt{3x}dx
f(t)=2cos(2t)	f(t)=2\cos(2t)
derivative of f(x)= 1/(\sqrt[3]{x^2)}	derivative\:f(x)=\frac{1}{\sqrt[3]{x^{2}}}
integral of ()/1	\int\:\frac{dy}{1}dx
derivative of-1/(2sqrt(x))	\frac{d}{dx}(-\frac{1}{2\sqrt{x}})
limit as x approaches 2 of f(x)+5g(x)	\lim\:_{x\to\:2}(f(x)+5g(x))
integral from 0 to 9 of 1/(sqrt(81-t^2))	\int\:_{0}^{9}\frac{1}{\sqrt{81-t^{2}}}dt
integral of sin(φ)	\int\:\sin(φ)dφ
derivative of sqrt(x+1)(x-1)	\frac{d}{dx}(\sqrt{x+1}(x-1))
limit as x approaches 0 of 1/(x^{13)}	\lim\:_{x\to\:0}(\frac{1}{x^{13}})
(x^2+1)(dy)/(dx)=x^2(y-1)	(x^{2}+1)\frac{dy}{dx}=x^{2}(y-1)
derivative of xysqrt(1-(x^2/4-(y^2)/9))	\frac{d}{dx}(xy\sqrt{1-\frac{x^{2}}{4}-\frac{y^{2}}{9}})
derivative of f(x)=(x^3+2x^2+x-1)/x	derivative\:f(x)=\frac{x^{3}+2x^{2}+x-1}{x}
sum from n=0 to infinity of (-1)^n(2)^n	\sum\:_{n=0}^{\infty\:}(-1)^{n}(2)^{n}
area f(x)=x^2-2,-3,1	area\:f(x)=x^{2}-2,-3,1
xy^{'''}+2y^{''}=6x	xy^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}=6x
integral of (x^4+x^3+2x+1)/(x^2+x)	\int\:\frac{x^{4}+x^{3}+2x+1}{x^{2}+x}dx
derivative of (x^2+5/(x^2-1))	\frac{d}{dx}(\frac{x^{2}+5}{x^{2}-1})
derivative of 2x^2+4x-1	\frac{d}{dx}(2x^{2}+4x-1)
integral from 0 to 1 of (61)/(4y-1)	\int\:_{0}^{1}\frac{61}{4y-1}dy
implicit (dy)/(dx),ln(x^2-24y)=x-y-4	implicit\:\frac{dy}{dx},\ln(x^{2}-24y)=x-y-4
tangent of f(x)=-2-6x^2,(5,-152)	tangent\:f(x)=-2-6x^{2},(5,-152)
integral of sin(x)cos^2(x)	\int\:\sin(x)\cos^{2}(x)dx
inverse oflaplace (3s-4)/(s^2+4s+8)	inverselaplace\:\frac{3s-4}{s^{2}+4s+8}
d/(dy)((y-6)/(y^2-2y+12))	\frac{d}{dy}(\frac{y-6}{y^{2}-2y+12})
integral of (e^{3x}+1)^2	\int\:(e^{3x}+1)^{2}dx
y^{''}+2y^'-3=0	y^{\prime\:\prime\:}+2y^{\prime\:}-3=0
limit as x approaches-5-of (3x)/(2x+10)	\lim\:_{x\to\:-5-}(\frac{3x}{2x+10})
limit as x approaches 0-of (1/5)^{1/x}	\lim\:_{x\to\:0-}((\frac{1}{5})^{\frac{1}{x}})
limit as x approaches 1-0 of 1/(1-x)	\lim\:_{x\to\:1-0}(\frac{1}{1-x})
limit as x approaches infinity+of xln(x)	\lim\:_{x\to\:\infty\:+}(x\ln(x))
derivative of f(x)=x^3-7x^2+6x+1	derivative\:f(x)=x^{3}-7x^{2}+6x+1
integral of e^{x^3}x	\int\:e^{x^{3}}xdx
integral of (3-x)/(sqrt(1-x^2))	\int\:\frac{3-x}{\sqrt{1-x^{2}}}dx
derivative of x^2+ln(x)	\frac{d}{dx}(x^{2}+\ln(x))
(\partial)/(\partial t)(te^{w/t})	\frac{\partial\:}{\partial\:t}(te^{\frac{w}{t}})
integral of x(4x+1)	\int\:x(4x+1)dx
(df)/(dt)=4t+(9t)/(sqrt(9-t^2))	\frac{df}{dt}=4t+\frac{9t}{\sqrt{9-t^{2}}}
roots x*y^2	roots\:x\cdot\:y^{2}
limit as x approaches 3 of-sqrt(x+3)	\lim\:_{x\to\:3}(-\sqrt{x+3})
derivative of sqrt((x^2-1/(x^2-2x+1)))	\frac{d}{dx}(\sqrt{\frac{x^{2}-1}{x^{2}-2x+1}})
integral of 2sqrt(s)	\int\:2\sqrt{s}ds
integral of (29)/(29+e^x)	\int\:\frac{29}{29+e^{x}}dx
(\partial)/(\partial x)(yze^{xz}+40)	\frac{\partial\:}{\partial\:x}(yze^{xz}+40)
derivative of log_{4}(xe^x)	\frac{d}{dx}(\log_{4}(xe^{x}))
y^{''}+9y=4sec(3t)	y^{\prime\:\prime\:}+9y=4\sec(3t)
(dy)/(dx)+(2y)/(x+4)=(x+4)^7	\frac{dy}{dx}+\frac{2y}{x+4}=(x+4)^{7}
integral of (x^4)/(x^2+4x+4)	\int\:\frac{x^{4}}{x^{2}+4x+4}dx
integral of 5sec^6(x)	\int\:5\sec^{6}(x)dx
integral of x/(sqrt(3x+1))	\int\:\frac{x}{\sqrt{3x+1}}dx
integral from 3 to 8 of x/(x^2-1)	\int\:_{3}^{8}\frac{x}{x^{2}-1}dx
integral of cos(x-2y)	\int\:\cos(x-2y)dx
integral from 0 to infinity of xe^{-x/3}	\int\:_{0}^{\infty\:}xe^{-\frac{x}{3}}dx
area x^2,sqrt(6+x)	area\:x^{2},\sqrt{6+x}
integral of sin^3(x/(10))cos^2(x/(10))	\int\:\sin^{3}(\frac{x}{10})\cos^{2}(\frac{x}{10})dx
y^{''}+12y^'+35y=70t^2+48t+4+48e^t	y^{\prime\:\prime\:}+12y^{\prime\:}+35y=70t^{2}+48t+4+48e^{t}
laplacetransform h(t)=-5t^2	laplacetransform\:h(t)=-5t^{2}
derivative of (5sin(x)/(3+cos(x)))	\frac{d}{dx}(\frac{5\sin(x)}{3+\cos(x)})
integral from 0 to 5/2 of 1/(25+4x^2)	\int\:_{0}^{\frac{5}{2}}\frac{1}{25+4x^{2}}dx
integral of 3x^2-12x+12	\int\:3x^{2}-12x+12dx
integral from 1 to 4 of (2x+sqrt(x))	\int\:_{1}^{4}(2x+\sqrt{x})dx
integral of ln(n)	\int\:\ln(n)
integral of (2e^{3t})/(1+e^{6t)}	\int\:\frac{2e^{3t}}{1+e^{6t}}dt

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