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Popular Calculus Problems

area y=(x^2)/2-4x+6,y= x/2-1,x=0,x=5	area\:y=\frac{x^{2}}{2}-4x+6,y=\frac{x}{2}-1,x=0,x=5
integral of (441)/(x^3-21x^2)	\int\:\frac{441}{x^{3}-21x^{2}}dx
integral of (x^2)/((25+x^2)^2)	\int\:\frac{x^{2}}{(25+x^{2})^{2}}dx
5sqrt(xy)(dy)/(dx)=1	5\sqrt{xy}\frac{dy}{dx}=1
y^{''}-3y^'-12y=0	y^{\prime\:\prime\:}-3y^{\prime\:}-12y=0
inverse oflaplace (4e^{(-2s)})/((s^2-4s+3))	inverselaplace\:\frac{4e^{(-2s)}}{(s^{2}-4s+3)}
derivative of sqrt(x^2+2x-3)	\frac{d}{dx}(\sqrt{x^{2}+2x-3})
integral of (arctan(9x))/(1+81x^2)	\int\:\frac{\arctan(9x)}{1+81x^{2}}dx
integral of (300)/(x^2sqrt(100-x^2))	\int\:\frac{300}{x^{2}\sqrt{100-x^{2}}}dx
(\partial)/(\partial x)(cos^5(x^6y^7))	\frac{\partial\:}{\partial\:x}(\cos^{5}(x^{6}y^{7}))
derivative of y=10(3x+1)(1-5x)	derivative\:y=10(3x+1)(1-5x)
integral of arccot(3y)	\int\:\arccot(3y)dy
derivative of x-\sqrt[5]{1+x^5-6x^{10}}	\frac{d}{dx}(x-\sqrt[5]{1+x^{5}-6x^{10}})
integral of x^3sqrt(x)	\int\:x^{3}\sqrt{x}dx
integral from 0 to 1 of (12)/(4x^2+5x+1)	\int\:_{0}^{1}\frac{12}{4x^{2}+5x+1}dx
limit as x approaches 2 of x(x-4)	\lim\:_{x\to\:2}(x(x-4))
derivative of x^2(1-xsqrt(x))	\frac{d}{dx}(x^{2}(1-x\sqrt{x}))
limit as x approaches infinity+of x^2e^x	\lim\:_{x\to\:\infty\:+}(x^{2}e^{x})
integral of sin^2(2t)	\int\:\sin^{2}(2t)dt
integral from 0 to 5 of x^3sqrt(1+9x^4)	\int\:_{0}^{5}x^{3}\sqrt{1+9x^{4}}dx
integral of (4x+2)/(e^x)	\int\:\frac{4x+2}{e^{x}}dx
integral of 1/(cos^2(t))	\int\:\frac{1}{\cos^{2}(t)}dt
derivative of f(x)=2x^3+x	derivative\:f(x)=2x^{3}+x
(dy)/(dx)+y^7x+3y=0	\frac{dy}{dx}+y^{7}x+3y=0
y^'=(xe^x)/(2y)	y^{\prime\:}=\frac{xe^{x}}{2y}
limit as x approaches 0 of sin(1/2)	\lim\:_{x\to\:0}(\sin(\frac{1}{2}))
integral of (9x^2)/(x^3+8)	\int\:\frac{9x^{2}}{x^{3}+8}dx
integral of ((x^2-8))/(8x)	\int\:\frac{(x^{2}-8)}{8x}dx
integral from 0 to 2 of (x^3-6x^2+8x)	\int\:_{0}^{2}(x^{3}-6x^{2}+8x)dx
integral from 0 to 1 of 6cos(x^2)	\int\:_{0}^{1}6\cos(x^{2})dx
(\partial)/(\partial x)(4x^3-4y)	\frac{\partial\:}{\partial\:x}(4x^{3}-4y)
(dy}{dx}+\frac{3y)/x =6x^2	\frac{dy}{dx}+\frac{3y}{x}=6x^{2}
derivative of sin(2t)	derivative\:\sin(2t)
(\partial)/(\partial x)(x^{0.75})	\frac{\partial\:}{\partial\:x}(x^{0.75})
y^{''}+2y^'-y=0,y(0)=0,y^'(0)=2sqrt(2)	y^{\prime\:\prime\:}+2y^{\prime\:}-y=0,y(0)=0,y^{\prime\:}(0)=2\sqrt{2}
limit as x approaches 1/2 of 3x-5	\lim\:_{x\to\:\frac{1}{2}}(3x-5)
integral of (x^2-2x+5)/(sqrt(9-x^2))	\int\:\frac{x^{2}-2x+5}{\sqrt{9-x^{2}}}dx
tangent of y=-x^2,(8,-64)	tangent\:y=-x^{2},(8,-64)
area e^x,e^{-4x},ln(4)	area\:e^{x},e^{-4x},\ln(4)
integral of-x^2+x+6	\int\:-x^{2}+x+6dx
area y=sqrt(x+3),x=-3,y=5	area\:y=\sqrt{x+3},x=-3,y=5
(\partial)/(\partial x)(2000e^{(x)(y)})	\frac{\partial\:}{\partial\:x}(2000e^{(x)(y)})
derivative of sqrt(t^2+a^2)	derivative\:\sqrt{t^{2}+a^{2}}
derivative of x^4e^{10x}	\frac{d}{dx}(x^{4}e^{10x})
derivative of 8/5 x^{-2/4}	\frac{d}{dx}(\frac{8}{5}x^{-\frac{2}{4}})
tangent of f(x)=x^3+2x,\at x=3	tangent\:f(x)=x^{3}+2x,\at\:x=3
limit as x approaches 1 of 7	\lim\:_{x\to\:1}(7)
maclaurin x^4	maclaurin\:x^{4}
area v(t)=sqrt(t)-13,[0,3]	area\:v(t)=\sqrt{t}-13,[0,3]
integral of (3x+2)/(x+1)	\int\:\frac{3x+2}{x+1}dx
area 2x^3+10x^2+22x-3,x^3-x^2-6x-3,-2,-2	area\:2x^{3}+10x^{2}+22x-3,x^{3}-x^{2}-6x-3,-2,-2
derivative of 2/((1+x^3))	\frac{d}{dx}(\frac{2}{(1+x)^{3}})
tangent of y=x^2+x,(1,2)	tangent\:y=x^{2}+x,(1,2)
tangent of f(x)=-3cos(x),\at x= pi/2	tangent\:f(x)=-3\cos(x),\at\:x=\frac{π}{2}
area x^2+12x,3x^2+10,1,4	area\:x^{2}+12x,3x^{2}+10,1,4
integral of 1/((y^2+z^2)^{3/2)}	\int\:\frac{1}{(y^{2}+z^{2})^{\frac{3}{2}}}dy
y^{''}-4y^'+4y=3x^2+2xe^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=3x^{2}+2xe^{2x}
sum from n=9 to infinity of e^{3-2n}	\sum\:_{n=9}^{\infty\:}e^{3-2n}
inverse oflaplace 1/(1+x)	inverselaplace\:\frac{1}{1+x}
integral of sqrt(5x-3)	\int\:\sqrt{5x-3}dx
limit as x approaches 0 of e^{pi(x+1)}	\lim\:_{x\to\:0}(e^{π(x+1)})
y^'=2xy^2+3x^2y^2	y^{\prime\:}=2xy^{2}+3x^{2}y^{2}
limit as x approaches-7 of 1/(x^2(x+7))	\lim\:_{x\to\:-7}(\frac{1}{x^{2}(x+7)})
x^{''}+x=e^{2t}	x^{\prime\:\prime\:}+x=e^{2t}
(\partial)/(\partial x)(ln(x+8y+4z))	\frac{\partial\:}{\partial\:x}(\ln(x+8y+4z))
limit as x approaches 0 of ln(x+1)	\lim\:_{x\to\:0}(\ln(x+1))
derivative of (6xh+3h^2)/h	derivative\:\frac{6xh+3h^{2}}{h}
derivative of f(x)=-e^x	derivative\:f(x)=-e^{x}
integral of sin(2θ)e^{sin^2(θ)}	\int\:\sin(2θ)e^{\sin^{2}(θ)}dθ
(\partial)/(\partial x)(In\|x-y\|)	\frac{\partial\:}{\partial\:x}(In\left\|x-y\right\|)
limit as x approaches 2 of e^{3/((2-x))}	\lim\:_{x\to\:2}(e^{\frac{3}{(2-x)}})
derivative of sqrt((5x^3)/(2x-2))	derivative\:\sqrt{\frac{5x^{3}}{2x-2}}
y^{''}-y^'-12y=2e^{3x}	y^{\prime\:\prime\:}-y^{\prime\:}-12y=2e^{3x}
(\partial)/(\partial v)({u}(v)(v)^2e^{-v})	\frac{\partial\:}{\partial\:v}({u}(v)(v)^{2}e^{-v})
derivative of 3x^5e^{2x}	\frac{d}{dx}(3x^{5}e^{2x})
limit as x approaches-7 of (x+7)/(\|x+7\|)	\lim\:_{x\to\:-7}(\frac{x+7}{\left\|x+7\right\|})
integral from 1 to e of ln(10x)	\int\:_{1}^{e}\ln(10x)dx
derivative of y=sin^2(4pit-5)	derivative\:y=\sin^{2}(4πt-5)
derivative of x^pi	\frac{d}{dx}(x^{π})
derivative of sqrt(x^2-4)+sqrt(4-y^2)	\frac{d}{dx}(\sqrt{x^{2}-4}+\sqrt{4-y^{2}})
integral of x^2(x^3+1)^4	\int\:x^{2}(x^{3}+1)^{4}dx
(\partial)/(\partial x)(x^2+y^2+48-xy-6x)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+48-xy-6x)
derivative of (cos(x))/(x^7)	derivative\:\frac{\cos(x)}{x^{7}}
tangent of f(x)=x^2-3x	tangent\:f(x)=x^{2}-3x
integral of 21te^t	\int\:21te^{t}dt
integral of 3xsqrt(x^2+4)	\int\:3x\sqrt{x^{2}+4}dx
derivative of e^{-5x}cos(3x)	\frac{d}{dx}(e^{-5x}\cos(3x))
integral of ln(7x+1)	\int\:\ln(7x+1)dx
derivative of (3x^5-1(2-x^4))	\frac{d}{dx}((3x^{5}-1)(2-x^{4}))
derivative of y=xsqrt(x+1)	derivative\:y=x\sqrt{x+1}
integral of 2x^3sqrt(x^2-1)	\int\:2x^{3}\sqrt{x^{2}-1}dx
integral of 7e^{-0.2x}	\int\:7e^{-0.2x}dx
derivative of (6x/(9-tan(x)))	\frac{d}{dx}(\frac{6x}{9-\tan(x)})
derivative of e^{tan(pix})	\frac{d}{dx}(e^{\tan(πx)})
integral of (40)/(40+e^x)	\int\:\frac{40}{40+e^{x}}dx
f(x)=2e^{x-1}	f(x)=2e^{x-1}
integral of 9/(x+1)	\int\:\frac{9}{x+1}dx
derivative of 3(-csc^2(x+sec^2(x)))	\frac{d}{dx}(3(-\csc^{2}(x)+\sec^{2}(x)))
area y=7x^2,y^2= 1/7 x	area\:y=7x^{2},y^{2}=\frac{1}{7}x
taylor 1/(sqrt(1+x))	taylor\:\frac{1}{\sqrt{1+x}}

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