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Popular Calculus Problems

derivative of (1+sqrt(x)(x^3))	\frac{d}{dx}((1+\sqrt{x})(x^{3}))
(\partial)/(\partial y)(x^{1/3}y^{2/3})	\frac{\partial\:}{\partial\:y}(x^{\frac{1}{3}}y^{\frac{2}{3}})
integral of (x^2+6x+2)/(x^3+9x^2+6x+9)	\int\:\frac{x^{2}+6x+2}{x^{3}+9x^{2}+6x+9}dx
y^'+0.06y=6	y^{\prime\:}+0.06y=6
sum from n=1 to infinity of ((n!))/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{(n!)}{n^{n}}
derivative of y=91	derivative\:y=91
integral of x^2(x+1)	\int\:x^{2}(x+1)dx
limit as x approaches-3 of (x+3)/(x+4)	\lim\:_{x\to\:-3}(\frac{x+3}{x+4})
integral of ((1+cos(x)))/(sin(x))	\int\:\frac{(1+\cos(x))}{\sin(x)}dx
(\partial)/(\partial x)(e^x+y+y^4+6)	\frac{\partial\:}{\partial\:x}(e^{x}+y+y^{4}+6)
y^{''}+3/x y^'-8/(x^2)y=0	y^{\prime\:\prime\:}+\frac{3}{x}y^{\prime\:}-\frac{8}{x^{2}}y=0
integral from-5 to 5 of 1/x	\int\:_{-5}^{5}\frac{1}{x}dx
y^{''}+10y^'+25y=t^{-2}e^{-5t}	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=t^{-2}e^{-5t}
(\partial)/(\partial x)(e^{2x}cos(3y))	\frac{\partial\:}{\partial\:x}(e^{2x}\cos(3y))
derivative of x(4x-5^3)	\frac{d}{dx}(x(4x-5)^{3})
integral from 0 to 2 of 4xe^x	\int\:_{0}^{2}4xe^{x}dx
limit as x approaches 1 of (4x+3)/(2x+1)	\lim\:_{x\to\:1}(\frac{4x+3}{2x+1})
sum from n=1 to infinity of 4*(4/7)^n	\sum\:_{n=1}^{\infty\:}4\cdot\:(\frac{4}{7})^{n}
integral of ((x(x-8))/(x+1))^2	\int\:(\frac{x(x-8)}{x+1})^{2}dx
derivative of f(x)=5x(sin(x)+cos(x))	derivative\:f(x)=5x(\sin(x)+\cos(x))
integral of sin(pi+2y)-sin(2y)	\int\:\sin(π+2y)-\sin(2y)dy
(\partial)/(\partial y)(xye^y+e^ysin(x))	\frac{\partial\:}{\partial\:y}(xye^{y}+e^{y}\sin(x))
(\partial)/(\partial x)(sqrt(16-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{16-x^{2}-y^{2}})
area y=e^{-2x}+1,y=0,x=0,x=3	area\:y=e^{-2x}+1,y=0,x=0,x=3
(\partial)/(\partial t)(3e^{sin(x+4ct)})	\frac{\partial\:}{\partial\:t}(3e^{\sin(x+4ct)})
f(x)=x^{6x}	f(x)=x^{6x}
y^'=((4x^3+y^3))/(xy^2)	y^{\prime\:}=\frac{(4x^{3}+y^{3})}{xy^{2}}
sum from n=0 to infinity of 1/(2n!)	\sum\:_{n=0}^{\infty\:}\frac{1}{2n!}
y^'=cos^2(y)ln(x)	y^{\prime\:}=\cos^{2}(y)\ln(x)
(\partial)/(\partial x)(e^{5x}sin(5y))	\frac{\partial\:}{\partial\:x}(e^{5x}\sin(5y))
longdivision (x^2-1)/(x^2+x+1)	longdivision\:\frac{x^{2}-1}{x^{2}+x+1}
derivative of y=-2/(x^2)	derivative\:y=-\frac{2}{x^{2}}
derivative of 2sin(4pi(x+1/8))	derivative\:2\sin(4π(x+\frac{1}{8}))
integral of (x+1)/(sqrt(x-1))	\int\:\frac{x+1}{\sqrt{x-1}}dx
limit as x approaches-1 of 8x^3	\lim\:_{x\to\:-1}(8x^{3})
area 4x^2,x^4-6x^2,[-3,3]	area\:4x^{2},x^{4}-6x^{2},[-3,3]
limit as x approaches 0 of (sin(pi+x))/x	\lim\:_{x\to\:0}(\frac{\sin(π+x)}{x})
area y=12,y=2x^2-11x+12	area\:y=12,y=2x^{2}-11x+12
f(x)=2x^7-3x^6+3x^3-4x^2-7	f(x)=2x^{7}-3x^{6}+3x^{3}-4x^{2}-7
derivative of ln(x^2(3x^2+6))	\frac{d}{dx}(\ln(x^{2})(3x^{2}+6))
integral from 2 to 5 of (-3v+4)	\int\:_{2}^{5}(-3v+4)dv
(dy)/(dx)=((x^2-y^2))/(3xy)	\frac{dy}{dx}=\frac{(x^{2}-y^{2})}{3xy}
integral of 10xsec^2(x)	\int\:10x\sec^{2}(x)dx
limit as x approaches-6 of (x^2-1)/(6-x)	\lim\:_{x\to\:-6}(\frac{x^{2}-1}{6-x})
derivative of (e^{3x^2}/(5x))	\frac{d}{dx}(\frac{e^{3x^{2}}}{5x})
derivative of f(x)=16\sqrt[4]{x}	derivative\:f(x)=16\sqrt[4]{x}
integral of (sin^7(10x))/(cos^4(10x))	\int\:\frac{\sin^{7}(10x)}{\cos^{4}(10x)}dx
(\partial)/(\partial y)({f}(x,y)(x+y))	\frac{\partial\:}{\partial\:y}({f}(x,y)(x+y))
derivative of f(x)=sqrt(x+13)	derivative\:f(x)=\sqrt{x+13}
xy^'-y=-2x^2-2x+1	xy^{\prime\:}-y=-2x^{2}-2x+1
(\partial)/(\partial z)(xy^2e^y)	\frac{\partial\:}{\partial\:z}(xy^{2}e^{y})
derivative of y=(3-e^{-x})^2	\frac{d}{dx}y=(3-e^{-x})^{2}
integral of 1/(4x-10)	\int\:\frac{1}{4x-10}dx
(\partial)/(\partial x)(sin^2(θ))	\frac{\partial\:}{\partial\:x}(\sin^{2}(θ))
area x=-5,x=1,y=2x^2+4,y=0	area\:x=-5,x=1,y=2x^{2}+4,y=0
integral from-1 to 1 of x+1	\int\:_{-1}^{1}x+1dx
limit as x approaches 0+of sqrt(1/x)	\lim\:_{x\to\:0+}(\sqrt{\frac{1}{x}})
integral from 0 to (3pi)/2 of cos^3(33x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(33x)dx
integral from 0 to 1/2 of 1/(1+4x^2)	\int\:_{0}^{\frac{1}{2}}\frac{1}{1+4x^{2}}dx
(\partial)/(\partial y)((x^2)/(y+2))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}}{y+2})
derivative of tan(2x^3)	\frac{d}{dx}(\tan(2x^{3}))
integral of x/(sqrt(x^4-16x^2+39))	\int\:\frac{x}{\sqrt{x^{4}-16x^{2}+39}}dx
area y=x+x^2+x^3,x=1	area\:y=x+x^{2}+x^{3},x=1
integral from 0 to e of a^x	\int\:_{0}^{e}a^{x}dx
(\partial)/(\partial v)(u^2-v^2)	\frac{\partial\:}{\partial\:v}(u^{2}-v^{2})
integral of-3cos(2x)	\int\:-3\cos(2x)dx
integral of (2^{sqrt(x)})/(sqrt(x))	\int\:\frac{2^{\sqrt{x}}}{\sqrt{x}}dx
integral of 1-6x	\int\:1-6xdx
integral from 0 to pi/4 of cot(x)	\int\:_{0}^{\frac{π}{4}}\cot(x)dx
tangent of f(x)=5x-4x^2,(-1,-9)	tangent\:f(x)=5x-4x^{2},(-1,-9)
sum from n=0 to infinity of 5/(2+3^n)	\sum\:_{n=0}^{\infty\:}\frac{5}{2+3^{n}}
integral of (csc(x)cot(x))/(2-csc(x))	\int\:\frac{\csc(x)\cot(x)}{2-\csc(x)}dx
integral of e^{-x}(9+e^{-x})	\int\:e^{-x}(9+e^{-x})dx
limit as y approaches 6 of (2y^2-15y+18)/(3y^2-17y-6)	\lim\:_{y\to\:6}(\frac{2y^{2}-15y+18}{3y^{2}-17y-6})
integral of x^{1/7}	\int\:x^{\frac{1}{7}}dx
integral of (81)/(x^4+27x)	\int\:\frac{81}{x^{4}+27x}dx
derivative of-7x^2+400x	\frac{d}{dx}(-7x^{2}+400x)
y^{''}-4y=8e^{2x}	y^{\prime\:\prime\:}-4y=8e^{2x}
limit as x approaches 3 of x+12	\lim\:_{x\to\:3}(x+12)
integral from 0 to 2pi of sin(θ)	\int\:_{0}^{2π}\sin(θ)dθ
(dy)/(dx)=e^{x+y+3}	\frac{dy}{dx}=e^{x+y+3}
tangent of 4x^3-13x^2+4	tangent\:4x^{3}-13x^{2}+4
derivative of 9(sin(x)+xcos(x))	derivative\:9(\sin(x)+x\cos(x))
derivative of f(t)=(3t-2)^5	derivative\:f(t)=(3t-2)^{5}
area y=x^3,0<= x<= 5	area\:y=x^{3},0\le\:x\le\:5
(\partial)/(\partial y)((xy)/(cos(x)))	\frac{\partial\:}{\partial\:y}(\frac{xy}{\cos(x)})
inverse oflaplace s^2+4s+13	inverselaplace\:s^{2}+4s+13
(\partial)/(\partial z)(cos(z){w}(z))	\frac{\partial\:}{\partial\:z}(\cos(z){w}(z))
(dy)/(dt)=2(1-y),y(0)=0	\frac{dy}{dt}=2(1-y),y(0)=0
tangent of y=(8x)/(x^2+1),(0,0)	tangent\:y=\frac{8x}{x^{2}+1},(0,0)
(x^4+1)dy+x(1+4y^2)dx=0	(x^{4}+1)dy+x(1+4y^{2})dx=0
sum from n=0 to infinity of (n^2)/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}}{5^{n}}
integral of e^{-2s}	\int\:e^{-2s}ds
laplacetransform 1	laplacetransform\:1
derivative of-(18/(x^4))	\frac{d}{dx}(-\frac{18}{x^{4}})
limit as x approaches 13 of 4	\lim\:_{x\to\:13}(4)
derivative of sqrt(11x+2)	\frac{d}{dx}(\sqrt{11x+2})
integral of (cos(x))/(2-sin(x))	\int\:\frac{\cos(x)}{2-\sin(x)}dx
y^{''}+4y^'+3y=sqrt(x)	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=\sqrt{x}
derivative of 3/(2-2x^2)	derivative\:\frac{3}{2-2x^{2}}

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