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Popular Calculus Problems

(\partial)/(\partial x)(ln(x^7+y^7))	\frac{\partial\:}{\partial\:x}(\ln(x^{7}+y^{7}))
integral from-1 to 3 of (x^3)/4+x^2-5/4	\int\:_{-1}^{3}\frac{x^{3}}{4}+x^{2}-\frac{5}{4}dx
integral of ln(1+x)	\int\:\ln(1+x)dx
d/(dy)((y-1)/(y^2-y+1))	\frac{d}{dy}(\frac{y-1}{y^{2}-y+1})
integral from 1 to 2 of 2(x^2-4)	\int\:_{1}^{2}2(x^{2}-4)dx
integral of (y+13)/((y+1)(y+3)(y-2))	\int\:\frac{y+13}{(y+1)(y+3)(y-2)}dy
integral of 1/(sqrt(-t^2+8t-12))	\int\:\frac{1}{\sqrt{-t^{2}+8t-12}}dt
(e^x+e^{-x})((dy)/(dx))=y^2	(e^{x}+e^{-x})(\frac{dy}{dx})=y^{2}
taylor x^{-2},2	taylor\:x^{-2},2
integral of (cos^3(x))/(sin^8(x))	\int\:\frac{\cos^{3}(x)}{\sin^{8}(x)}dx
derivative of y=7x*ln(5x)-7x	derivative\:y=7x\cdot\:\ln(5x)-7x
derivative of ((x+2^2)/(1-x))	\frac{d}{dx}(\frac{(x+2)^{2}}{1-x})
integral of (1/(3x))	\int\:(\frac{1}{3x})dx
derivative of ln(x^2+3x+5)	\frac{d}{dx}(\ln(x^{2}+3x+5))
integral of 10x^4	\int\:10x^{4}dx
area y=25-x^2,(0,5)	area\:y=25-x^{2},(0,5)
derivative of (t^2+9)e^t	derivative\:(t^{2}+9)e^{t}
inverse oflaplace (-4e^{(-s)})/((s^2-4s+3))	inverselaplace\:\frac{-4e^{(-s)}}{(s^{2}-4s+3)}
y^'=(t+y)^2-1,y(2)=4	y^{\prime\:}=(t+y)^{2}-1,y(2)=4
integral of x(x-1)^3	\int\:x(x-1)^{3}dx
derivative of x/(sqrt(81+x^2))	\frac{d}{dx}(\frac{x}{\sqrt{81+x^{2}}})
(\partial)/(\partial x)((9x+2y)^6)	\frac{\partial\:}{\partial\:x}((9x+2y)^{6})
limit as x approaches 0 of x^4cos(3/x)	\lim\:_{x\to\:0}(x^{4}\cos(\frac{3}{x}))
integral of (sin^2(3x))^2	\int\:(\sin^{2}(3x))^{2}dx
d/(dt)(sinh(t))	\frac{d}{dt}(\sinh(t))
laplacetransform e^{4t}(5t^4+9t^3+11t)	laplacetransform\:e^{4t}(5t^{4}+9t^{3}+11t)
tangent of y= 1/(x^2),(1,1)	tangent\:y=\frac{1}{x^{2}},(1,1)
integral of z^nln(z)	\int\:z^{n}\ln(z)dz
(\partial)/(\partial x)(e^{x+y}sin(x-y))	\frac{\partial\:}{\partial\:x}(e^{x+y}\sin(x-y))
derivative of 2/3 (e^{-2x}+e^x)	\frac{d}{dx}(\frac{2}{3}(e^{-2x}+e^{x}))
derivative of (x^4)/(2-x^3)	derivative\:\frac{x^{4}}{2-x^{3}}
derivative of 47x^3-75sqrt(x)	\frac{d}{dx}(47x^{3}-75\sqrt{x})
y^{''}+7y^'+10y=10te^{4t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=10te^{4t}
integral from 0 to 1 of (57)/(x^5)	\int\:_{0}^{1}\frac{57}{x^{5}}dx
integral of (2x)/((x^3-1))	\int\:\frac{2x}{(x^{3}-1)}dx
sum from n=0 to infinity of (-4)^n	\sum\:_{n=0}^{\infty\:}(-4)^{n}
derivative of sqrt(x)+1/(sqrt(x^3))	derivative\:\sqrt{x}+\frac{1}{\sqrt{x^{3}}}
integral of 1/(64e^{-6x)+e^{6x}}	\int\:\frac{1}{64e^{-6x}+e^{6x}}dx
derivative of 2sec(x/2)	\frac{d}{dx}(2\sec(\frac{x}{2}))
integral of 1/(3+x)	\int\:\frac{1}{3+x}dx
2y^'+5y=4	2y^{\prime\:}+5y=4
integral of cos(npi x/2)	\int\:\cos(nπ\frac{x}{2})dx
derivative of sqrt(6+5{f)(x})	\frac{d}{dx}(\sqrt{6+5{f}(x)})
integral from 0.1 to 0.2 of 600x	\int\:_{0.1}^{0.2}600xdx
limit as x approaches infinity of x-3	\lim\:_{x\to\:\infty\:}(x-3)
integral of 1/(cos^2(θ))	\int\:\frac{1}{\cos^{2}(θ)}dθ
derivative of y=e^xx^5+10e^xx^4+20e^xx^3	derivative\:y=e^{x}x^{5}+10e^{x}x^{4}+20e^{x}x^{3}
(dy)/(dt)=0.225-y/(200)	\frac{dy}{dt}=0.225-\frac{y}{200}
derivative of e^e	\frac{d}{dx}(e^{e})
integral of (x^2-4x+4)^{10}	\int\:(x^{2}-4x+4)^{10}dx
area 4sqrt(x),x	area\:4\sqrt{x},x
(dy)/(dt)=1500-3/170 y	\frac{dy}{dt}=1500-\frac{3}{170}y
derivative of (x-8/(5x^2e^x))	\frac{d}{dx}(\frac{x-8}{5x^{2}e^{x}})
derivative of (2x-6)^4(x^2+x+1)^5	derivative\:(2x-6)^{4}(x^{2}+x+1)^{5}
integral of (10x-15)/(x^2+25)	\int\:\frac{10x-15}{x^{2}+25}dx
integral from 0 to pi/9 of xtan^2(3x)	\int\:_{0}^{\frac{π}{9}}x\tan^{2}(3x)dx
derivative of (ln(sin(x^2+1))/({f)(x)})	\frac{d}{dx}(\frac{\ln(\sin(x^{2})+1)}{{f}(x)})
tangent of y=x^2-2,(5,23)	tangent\:y=x^{2}-2,(5,23)
(\partial)/(\partial x)(3xyz)	\frac{\partial\:}{\partial\:x}(3xyz)
limit as x approaches 1+of x^{1/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{1}{1-x}})
integral of (2x)/(1-x^2)	\int\:\frac{2x}{1-x^{2}}dx
integral of (x^2+1)e^x	\int\:(x^{2}+1)e^{x}dx
integral from 4 to 20 of 1/16	\int\:_{4}^{20}\frac{1}{16}
integral of 1/([(x^2-9)^2])	\int\:\frac{1}{[(x^{2}-9)^{2}]}dx
limit as x approaches 0 of sin(2x)	\lim\:_{x\to\:0}(\sin(2x))
integral of (x^4)/((6-x^5)^2)	\int\:\frac{x^{4}}{(6-x^{5})^{2}}dx
derivative of e^{7x^2}	\frac{d}{dx}(e^{7x^{2}})
limit as x approaches-15+of (sqrt(x+15)+15)/(x^2-15)	\lim\:_{x\to\:-15+}(\frac{\sqrt{x+15}+15}{x^{2}-15})
integral from 0 to pi/2 of (cos(x))^7	\int\:_{0}^{\frac{π}{2}}(\cos(x))^{7}dx
integral of (x^8)/(24)	\int\:\frac{x^{8}}{24}dx
area 8-x^2,x^2	area\:8-x^{2},x^{2}
integral of-3/t	\int\:-\frac{3}{t}dt
integral of (x^2)/(x^2+64)	\int\:\frac{x^{2}}{x^{2}+64}dx
derivative of 10arccot(x)	\frac{d}{dx}(10\arccot(x))
integral of (-x)/(sqrt(4-x^2))	\int\:\frac{-x}{\sqrt{4-x^{2}}}dx
derivative of xy^2+x^2y^3+x^3y^4	\frac{d}{dx}(xy^{2}+x^{2}y^{3}+x^{3}y^{4})
tangent of x^2+y^2=25,(-3,4)	tangent\:x^{2}+y^{2}=25,(-3,4)
derivative of x^3(1-x^2)	\frac{d}{dx}(x^{3}(1-x)^{2})
integral of xsec^2(x)	\int\:x\sec^{2}(x)dx
integral of (sec^2(3)sqrt(t))/(sqrt(t))	\int\:\frac{\sec^{2}(3)\sqrt{t}}{\sqrt{t}}dt
derivative of y=(6x^2+2x+2)/(sqrt(x))	derivative\:y=\frac{6x^{2}+2x+2}{\sqrt{x}}
derivative of ln(4x^3-x^2)	\frac{d}{dx}(\ln(4x^{3}-x^{2}))
(\partial)/(\partial y)(xe^{x-y})	\frac{\partial\:}{\partial\:y}(xe^{x-y})
y^{''}+4y^'+24y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+24y=0
limit as x approaches 1 of x^2+5x-6	\lim\:_{x\to\:1}(x^{2}+5x-6)
(\partial)/(\partial y)(xsin(y))	\frac{\partial\:}{\partial\:y}(x\sin(y))
derivative of ((1+x)/((1-x)))	\frac{d}{dx}(\frac{(1+x)}{(1-x)})
(\partial)/(\partial x)(5xy(15-x-y))	\frac{\partial\:}{\partial\:x}(5xy(15-x-y))
derivative of 15e^{x^2}	derivative\:15e^{x^{2}}
y^'+2y=4sin(e^{2x})	y^{\prime\:}+2y=4\sin(e^{2x})
y^'=((e^{-x}-e^x))/((3+4y)),y(0)=1	y^{\prime\:}=\frac{(e^{-x}-e^{x})}{(3+4y)},y(0)=1
slope ofintercept (0,-9),(-1,-4)	slopeintercept\:(0,-9),(-1,-4)
(dy)/(dx)=cos^2(x)	\frac{dy}{dx}=\cos^{2}(x)
derivative of 2x^2sin(xtan(x))	\frac{d}{dx}(2x^{2}\sin(x)\tan(x))
integral of (8000ln(x+40))/((x+40)^2)	\int\:\frac{8000\ln(x+40)}{(x+40)^{2}}dx
integral from 0 to 2 of sqrt(10)	\int\:_{0}^{2}\sqrt{10}dx
integral of x^2-sqrt(4-x^2)	\int\:x^{2}-\sqrt{4-x^{2}}dx
(dy}{dx}=\frac{3x)/y	\frac{dy}{dx}=\frac{3x}{y}
derivative of sin(x*x^2)	\frac{d}{dx}(\sin(x)\cdot\:x^{2})
limit as x approaches 2 of cos(pi/2 x)	\lim\:_{x\to\:2}(\cos(\frac{π}{2}x))

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