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Popular Calculus Problems

integral from 2 to 4 of 1/((x-4)(x-1))	\int\:_{2}^{4}\frac{1}{(x-4)(x-1)}dx
integral from 9 to 16 of 1/(2-sqrt(x))	\int\:_{9}^{16}\frac{1}{2-\sqrt{x}}dx
(\partial)/(\partial y)(sin(y)+y,x)	\frac{\partial\:}{\partial\:y}(\sin(y)+y,x)
integral from 0 to 2 of te^t	\int\:_{0}^{2}te^{t}dt
area sin^2(x),sin^3(x),0,pi	area\:\sin^{2}(x),\sin^{3}(x),0,π
integral of 3sin(x)+2-3e^x	\int\:3\sin(x)+2-3e^{x}dx
area f(x)=4x(1-x),g(x)=4x-4	area\:f(x)=4x(1-x),g(x)=4x-4
derivative of 5x+(100/x)	\frac{d}{dx}(5x+\frac{100}{x})
limit as x approaches 2 of (x+2)/(x-2)	\lim\:_{x\to\:2}(\frac{x+2}{x-2})
derivative of 5/3	\frac{d}{dx}(\frac{5}{3})
derivative of (x^6/(12)ln(x)-(x^6)/(72))	\frac{d}{dx}(\frac{x^{6}}{12}\ln(x)-\frac{x^{6}}{72})
derivative of e^{-5x}-5e^{-5x}x	\frac{d}{dx}(e^{-5x}-5e^{-5x}x)
derivative of x*e^{-2x}	\frac{d}{dx}(x\cdot\:e^{-2x})
d/(d{x)}(({x})/((\|{y)\|-\|{z}\|)})	\frac{d}{d{x}}(\frac{{x}}{(\left\|{y}\right\|-\left\|{z}\right\|)})
integral of (x^4+x^2+1)/(x-1)	\int\:\frac{x^{4}+x^{2}+1}{x-1}dx
integral of (12)/(1+t^2)	\int\:\frac{12}{1+t^{2}}dt
laplacetransform-5sin(4t)	laplacetransform\:-5\sin(4t)
derivative of ((x-2(x^2-x+1))/(sqrt(x)))	\frac{d}{dx}(\frac{(x-2)(x^{2}-x+1)}{\sqrt{x}})
inverse oflaplace (s^3+5s^2+9s+7)/(s^2+3s+2)	inverselaplace\:\frac{s^{3}+5s^{2}+9s+7}{s^{2}+3s+2}
(\partial)/(\partial x)(ax^2)	\frac{\partial\:}{\partial\:x}(ax^{2})
limit as x approaches-3 of (x^2-4)/(3-x)	\lim\:_{x\to\:-3}(\frac{x^{2}-4}{3-x})
derivative of (x-4)/(x+2)	derivative\:\frac{x-4}{x+2}
integral of (2x+1)/((x-1)(x+4)^2)	\int\:\frac{2x+1}{(x-1)(x+4)^{2}}dx
integral of 1/(sqrt(x-1)-\sqrt{x)}	\int\:\frac{1}{\sqrt{x-1}-\sqrt{x}}dx
integral of (-2y)/x	\int\:\frac{-2y}{x}dx
limit as x approaches 5+of (-3)/(x^2-25)	\lim\:_{x\to\:5+}(\frac{-3}{x^{2}-25})
(1+x^2)y^'=x(1-y)	(1+x^{2})y^{\prime\:}=x(1-y)
area 1+4x-x^2,11-x-x^2,1-(2x)/3	area\:1+4x-x^{2},11-x-x^{2},1-\frac{2x}{3}
area sqrt(x+1),2x-4,0,3	area\:\sqrt{x+1},2x-4,0,3
integral of (3x^5-2)/(4x-4x^5)	\int\:\frac{3x^{5}-2}{4x-4x^{5}}dx
taylor 3/x ,-1	taylor\:\frac{3}{x},-1
derivative of 9sin(5x)	\frac{d}{dx}(9\sin(5x))
derivative of g(t)=2log_{5}(t)	derivative\:g(t)=2\log_{5}(t)
integral from 0 to 1 of 2/(sqrt(4-x^2))	\int\:_{0}^{1}\frac{2}{\sqrt{4-x^{2}}}dx
(\partial)/(\partial x)(x^{0.25}y^{0.25})	\frac{\partial\:}{\partial\:x}(x^{0.25}y^{0.25})
(dy)/(dx)=((y^3)/(x^2))	\frac{dy}{dx}=(\frac{y^{3}}{x^{2}})
integral of x(x^2+2)^6	\int\:x(x^{2}+2)^{6}dx
integral of-(y^2)/2	\int\:-\frac{y^{2}}{2}dy
derivative of (2x^2)/(6x+5)	derivative\:\frac{2x^{2}}{6x+5}
integral from 0 to ln(2) of e^{3x}	\int\:_{0}^{\ln(2)}e^{3x}dx
derivative of x/(sqrt(y))	\frac{d}{dx}(\frac{x}{\sqrt{y}})
integral of 4/(sqrt(x)(x+6))	\int\:\frac{4}{\sqrt{x}(x+6)}dx
y^'=(x^2+y^2)/(xy),y(1)=1	y^{\prime\:}=\frac{x^{2}+y^{2}}{xy},y(1)=1
sum from n=1 to infinity of 8(3/4)^n	\sum\:_{n=1}^{\infty\:}8(\frac{3}{4})^{n}
(\partial)/(\partial x)(4x^2y^2)	\frac{\partial\:}{\partial\:x}(4x^{2}y^{2})
slope of (-2,1),(3,-9)	slope\:(-2,1),(3,-9)
integral of 1/((r^2+x^2)^{3/2)}	\int\:\frac{1}{(r^{2}+x^{2})^{\frac{3}{2}}}dx
integral of xe^{1+x^2}	\int\:xe^{1+x^{2}}dx
integral of (x^3+x-1)/((x^2+2)^2)	\int\:\frac{x^{3}+x-1}{(x^{2}+2)^{2}}dx
integral of-csc^2((7x)/6)	\int\:-\csc^{2}(\frac{7x}{6})dx
integral from 0 to 5 of (8t)/((t-6)^2)	\int\:_{0}^{5}\frac{8t}{(t-6)^{2}}dt
integral of x^{2/5}	\int\:x^{\frac{2}{5}}dx
limit as x approaches-2 of e^{2x-x^2}	\lim\:_{x\to\:-2}(e^{2x-x^{2}})
derivative of-2x^{-2}	\frac{d}{dx}(-2x^{-2})
tangent of f(x)=(x-1)/(2-x),\at x=4	tangent\:f(x)=\frac{x-1}{2-x},\at\:x=4
integral of (x^3-3sqrt(x)+x^{-5/4})	\int\:(x^{3}-3\sqrt{x}+x^{-\frac{5}{4}})dx
x^{''}+2.25x^'+0.14x=0,x^'(0)=1,x(0)=2	x^{\prime\:\prime\:}+2.25x^{\prime\:}+0.14x=0,x^{\prime\:}(0)=1,x(0)=2
tangent of f(x)=x^3-2x^2-3x,(1,-4)	tangent\:f(x)=x^{3}-2x^{2}-3x,(1,-4)
(\partial)/(\partial x)(sqrt(xy)-z)	\frac{\partial\:}{\partial\:x}(\sqrt{xy}-z)
f(x)=7x^2	f(x)=7x^{2}
slope of (-5,2),(5,6)	slope\:(-5,2),(5,6)
inverse oflaplace t^{1/2}	inverselaplace\:t^{\frac{1}{2}}
derivative of tan(y/x)	\frac{d}{dx}(\tan(\frac{y}{x}))
limit as x approaches 6 of (x^2+11x-30)/(x^2-13x-42)	\lim\:_{x\to\:6}(\frac{x^{2}+11x-30}{x^{2}-13x-42})
derivative of csc^2(x)-1	derivative\:\csc^{2}(x)-1
area y=sqrt(x),y=2-x,y=0	area\:y=\sqrt{x},y=2-x,y=0
derivative of x^3y	derivative\:x^{3}y
derivative of 2/(2x+1)	derivative\:\frac{2}{2x+1}
tangent of sqrt(7x+1)	tangent\:\sqrt{7x+1}
integral of e^{3x}sin(7x)	\int\:e^{3x}\sin(7x)dx
integral from-1 to 4 of x+1	\int\:_{-1}^{4}x+1dx
derivative of 1/(xln(x))	derivative\:\frac{1}{x\ln(x)}
integral from 0 to pi of 17sin^2(4x)	\int\:_{0}^{π}17\sin^{2}(4x)dx
y^{'''}+4y^'=3x-1	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:}=3x-1
integral of (x^3-3x+\sqrt[4]{x}-5)	\int\:(x^{3}-3x+\sqrt[4]{x}-5)dx
tangent of y= 1/(5+2x),(-1, 1/3)	tangent\:y=\frac{1}{5+2x},(-1,\frac{1}{3})
x(dy)/(dx)=sqrt(x^2-y^2)+y	x\frac{dy}{dx}=\sqrt{x^{2}-y^{2}}+y
integral of-t	\int\:-tdt
limit as x approaches 3 of x(2/x+5)	\lim\:_{x\to\:3}(x(\frac{2}{x}+5))
integral from 1/7 to 5 of 12xln(7x)	\int\:_{\frac{1}{7}}^{5}12x\ln(7x)dx
derivative of y=e^{-4x}	derivative\:y=e^{-4x}
area x^3+8,x+8	area\:x^{3}+8,x+8
tangent of (6x)/((x^2+1))	tangent\:\frac{6x}{(x^{2}+1)}
(\partial)/(\partial y)((e^{xy})/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{e^{xy}}{x+y})
integral of 1/(sqrt(y^2+y+1))	\int\:\frac{1}{\sqrt{y^{2}+y+1}}dy
derivative of e^{ln(cos(x^2)}sqrt(2x+1))	\frac{d}{dx}(e^{\ln(\cos(x^{2}))}\sqrt{2x+1})
(dy)/(dx)+2xy=5x	\frac{dy}{dx}+2xy=5x
slope ofintercept (-4,-6),(-2,0)	slopeintercept\:(-4,-6),(-2,0)
sum from n=1 to infinity of n^5(1+n^6)^6	\sum\:_{n=1}^{\infty\:}n^{5}(1+n^{6})^{6}
derivative of ({f}(x)/(x^5))	\frac{d}{dx}(\frac{{f}(x)}{x^{5}})
derivative of (5x+2)^4(2x-3)^8	derivative\:(5x+2)^{4}(2x-3)^{8}
3*(dy)/(dx)+12y=4	3\cdot\:\frac{dy}{dx}+12y=4
(\partial)/(\partial x)(x^3z)	\frac{\partial\:}{\partial\:x}(x^{3}z)
limit as x approaches 1.2 of 1/(x-2)	\lim\:_{x\to\:1.2}(\frac{1}{x-2})
integral of ((x^2-x+6))/(x^3+3x)	\int\:\frac{(x^{2}-x+6)}{x^{3}+3x}dx
integral of pi*cos(pix)	\int\:π\cdot\:\cos(πx)dx
derivative of sqrt(5+xsec(x))	\frac{d}{dx}(\sqrt{5+x\sec(x)})
limit as x approaches 2 of 5x-3	\lim\:_{x\to\:2}(5x-3)
derivative of 1/(x-2)	derivative\:\frac{1}{x-2}
derivative of e^{nx}	\frac{d}{dx}(e^{nx})

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