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Popular Calculus Problems

maclaurin 2sin(x^2)	maclaurin\:2\sin(x^{2})
inverse oflaplace (2s^2+4s+5)/(s(s+1))	inverselaplace\:\frac{2s^{2}+4s+5}{s(s+1)}
derivative of x^3sin(x^2)	\frac{d}{dx}(x^{3}\sin(x^{2}))
x^2y^'+xy=2	x^{2}y^{\prime\:}+xy=2
derivative of-2x^4	derivative\:-2x^{4}
derivative of y= 6/x	derivative\:y=\frac{6}{x}
integral of ((3x+1)^{1/2})/2	\int\:\frac{(3x+1)^{\frac{1}{2}}}{2}dx
integral of sin^6(4x)	\int\:\sin^{6}(4x)dx
sum from n=0 to infinity of (1/8)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{8})^{n}
derivative of (e^{5x}/(x^{20)})	\frac{d}{dx}(\frac{e^{5x}}{x^{20}})
limit as x approaches 0+of ([x])/x	\lim\:_{x\to\:0+}(\frac{[x]}{x})
integral of x^4-x^2-x	\int\:x^{4}-x^{2}-xdx
integral of 6x^2sqrt(x+2)	\int\:6x^{2}\sqrt{x+2}dx
integral of (x^3+11)/(x^2+5x+6)	\int\:\frac{x^{3}+11}{x^{2}+5x+6}dx
(\partial)/(\partial x)(4x^3y^2-2)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{2}-2)
derivative of y=x^4-2x^3-9	derivative\:y=x^{4}-2x^{3}-9
integral of (sqrt(x)-1)	\int\:(\sqrt{x}-1)dx
limit as x approaches 0 of x/(1-x)	\lim\:_{x\to\:0}(\frac{x}{1-x})
(\partial)/(\partial x)(sin(x-3y))	\frac{\partial\:}{\partial\:x}(\sin(x-3y))
integral from-1 to 0 of (x+2)^{13}	\int\:_{-1}^{0}(x+2)^{13}dx
integral from 0 to infinity of-e^{-x}	\int\:_{0}^{\infty\:}-e^{-x}dx
tangent of f(x)=2x^2+2x,\at x=-2	tangent\:f(x)=2x^{2}+2x,\at\:x=-2
integral from-3 to 3 of (e^x-e^{-x})^2	\int\:_{-3}^{3}(e^{x}-e^{-x})^{2}dx
d/(dt)(cos(t)+tsin(t))	\frac{d}{dt}(\cos(t)+t\sin(t))
taylor ln((z+1/2)/z)	taylor\:\ln(\frac{z+\frac{1}{2}}{z})
sum from n=5 to infinity of 1/(4^n+1)	\sum\:_{n=5}^{\infty\:}\frac{1}{4^{n}+1}
inverse oflaplace z/((z+1)^2)	inverselaplace\:\frac{z}{(z+1)^{2}}
derivative of 8cos^3(t)	derivative\:8\cos^{3}(t)
derivative of f(x)=(4x)/((x^2+1))	derivative\:f(x)=\frac{4x}{(x^{2}+1)}
integral of x^{-1/4}	\int\:x^{-\frac{1}{4}}dx
(dy)/(dx)=8x^3y-8xy	\frac{dy}{dx}=8x^{3}y-8xy
integral of xsqrt(2x)	\int\:x\sqrt{2x}dx
integral of x(x+7)^{-3/2}	\int\:x(x+7)^{-\frac{3}{2}}dx
integral from-2 to 3 of 2/(x^4)	\int\:_{-2}^{3}\frac{2}{x^{4}}dx
integral of (2x+3)/(x^2+3x+3)	\int\:\frac{2x+3}{x^{2}+3x+3}dx
limit as x approaches-4 of x^2cos(5/x)	\lim\:_{x\to\:-4}(x^{2}\cos(\frac{5}{x}))
integral of (3tan(β)-4cos^2(β))/(cos(β))	\int\:\frac{3\tan(β)-4\cos^{2}(β)}{\cos(β)}dβ
(2sqrt(x)dy)/(dx)=sqrt(1-y^2)	\frac{2\sqrt{x}dy}{dx}=\sqrt{1-y^{2}}
area y=x^2-3,y=6	area\:y=x^{2}-3,y=6
area 4cos(7x),4-4cos(7x)	area\:4\cos(7x),4-4\cos(7x)
derivative of (t^2-2t)(t^2+2t)	derivative\:(t^{2}-2t)(t^{2}+2t)
(\partial)/(\partial x)(9y^4cos(x^2))	\frac{\partial\:}{\partial\:x}(9y^{4}\cos(x^{2}))
derivative of f(x)= 1/(x^2-9)	derivative\:f(x)=\frac{1}{x^{2}-9}
inverse oflaplace 1/2	inverselaplace\:\frac{1}{2}
integral of x^2*e^{-3x}	\int\:x^{2}\cdot\:e^{-3x}dx
(\partial)/(\partial x)(-ln(x))	\frac{\partial\:}{\partial\:x}(-\ln(x))
integral of (14)/(2x+xsqrt(x))	\int\:\frac{14}{2x+x\sqrt{x}}dx
y^{''}+4y^'+4y=xcos(2x)	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=x\cos(2x)
y^{''}+y^'+y=1	y^{\prime\:\prime\:}+y^{\prime\:}+y=1
(\partial)/(\partial x)(-xy^2z^3-4xyz)	\frac{\partial\:}{\partial\:x}(-xy^{2}z^{3}-4xyz)
sum from n=1 to infinity of sin^n(2)	\sum\:_{n=1}^{\infty\:}\sin^{n}(2)
area y=e^{-5x},x>= 0	area\:y=e^{-5x},x\ge\:0
limit as x approaches 2 of sqrt(4x-7)	\lim\:_{x\to\:2}(\sqrt{4x-7})
integral of 1/((z+1/2))	\int\:\frac{1}{(z+\frac{1}{2})}dz
integral of (cos^5(20))/(sqrt(sin(20)))0	\int\:\frac{\cos^{5}(20)}{\sqrt{\sin(20)}}d^{0}dd
limit as x approaches 0 of x/(arctan(6x))	\lim\:_{x\to\:0}(\frac{x}{\arctan(6x)})
limit as x approaches 0+of x^2+3x-4	\lim\:_{x\to\:0+}(x^{2}+3x-4)
derivative of (10/(1+e^{-x)})	\frac{d}{dx}(\frac{10}{1+e^{-x}})
(dy)/(dx)+(1/(200+3x))y=8	\frac{dy}{dx}+(\frac{1}{200+3x})y=8
-4xy^4=(dy)/(dx)	-4xy^{4}=\frac{dy}{dx}
integral of (e^{5x})/(e^{5x)+8}	\int\:\frac{e^{5x}}{e^{5x}+8}dx
derivative of (3x+1(5x-4))	\frac{d}{dx}((3x+1)(5x-4))
(\partial)/(\partial x)(cos(zw))	\frac{\partial\:}{\partial\:x}(\cos(zw))
sum from n=1 to infinity of (n!)/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{10^{n}}
derivative of (x^4-5x^3+sqrt(x))/(x^2)	derivative\:\frac{x^{4}-5x^{3}+\sqrt{x}}{x^{2}}
integral of (12)/(r^2+1)	\int\:\frac{12}{r^{2}+1}dr
integral of 1/(sqrt(100+x^2))	\int\:\frac{1}{\sqrt{100+x^{2}}}dx
derivative of (x+1(x-1)^2)	\frac{d}{dx}((x+1)(x-1)^{2})
integral of (e^{2x})/((1+e^{2x))^2}	\int\:\frac{e^{2x}}{(1+e^{2x})^{2}}dx
taylor 1/x	taylor\:\frac{1}{x}
integral of (4sqrt(x)-1/(2sqrt(x)))	\int\:(4\sqrt{x}-\frac{1}{2\sqrt{x}})dx
integral of 1/(y^2-16)	\int\:\frac{1}{y^{2}-16}dy
y^'=t^{1/4}-y	y^{\prime\:}=t^{\frac{1}{4}}-y
integral from-7 to 7 of (49-x^2)	\int\:_{-7}^{7}(49-x^{2})dx
derivative of ln((sqrt(x+3)/(e^{3x)}))	\frac{d}{dx}(\ln(\frac{\sqrt{x+3}}{e^{3x}}))
(\partial)/(\partial x)(x/(9+y))	\frac{\partial\:}{\partial\:x}(\frac{x}{9+y})
derivative of y=sqrt(7x^3-6x^2-8/x)	derivative\:y=\sqrt{7x^{3}-6x^{2}-\frac{8}{x}}
4y^{''}-y^'+y=0	4y^{\prime\:\prime\:}-y^{\prime\:}+y=0
y^{''}+2y^'-y=10	y^{\prime\:\prime\:}+2y^{\prime\:}-y=10
(dy)/(dx)=sqrt(1-9y^2),y(-1)=0	\frac{dy}{dx}=\sqrt{1-9y^{2}},y(-1)=0
limit as x approaches 0 of (\|sin(x)\|)/x	\lim\:_{x\to\:0}(\frac{\left\|\sin(x)\right\|}{x})
derivative of-(600/(x^2)+4)	\frac{d}{dx}(-\frac{600}{x^{2}}+4)
tangent of f(x)=4x-3x^2,\at x=2	tangent\:f(x)=4x-3x^{2},\at\:x=2
derivative of e^{,\at}sin(bt)	derivative\:e^{,\at\:}\sin(bt)
integral of csc(x)(csc(x)-cot(x))	\int\:\csc(x)(\csc(x)-\cot(x))dx
tangent of y=x^3-2x^2+5,(2,5)	tangent\:y=x^{3}-2x^{2}+5,(2,5)
x^2y^'+2xy=ln(x),y(1)=8	x^{2}y^{\prime\:}+2xy=\ln(x),y(1)=8
integral of x/((x+1)^2)	\int\:\frac{x}{(x+1)^{2}}dx
integral of (x+3)/(sqrt(x^2+4))	\int\:\frac{x+3}{\sqrt{x^{2}+4}}dx
integral of 1/(3sin(x)+4cos(x))	\int\:\frac{1}{3\sin(x)+4\cos(x)}dx
derivative of (5x^3+4^2)	\frac{d}{dx}((5x^{3}+4)^{2})
integral of (arctan(x))/(1+x^2)	\int\:\frac{\arctan(x)}{1+x^{2}}dx
7t*(dy)/(dt)+3y=sqrt(t)	7t\cdot\:\frac{dy}{dt}+3y=\sqrt{t}
integral of (2e^{2x})/(e^{2x)+14e^x+48}	\int\:\frac{2e^{2x}}{e^{2x}+14e^{x}+48}dx
(dy)/(dx)=3x^2(1+y^2)	\frac{dy}{dx}=3x^{2}(1+y^{2})
y^'=(4xsec(y/x)+y)/x	y^{\prime\:}=\frac{4x\sec(\frac{y}{x})+y}{x}
y^{''}+piy=0	y^{\prime\:\prime\:}+πy=0
integral of (cos^2(t))	\int\:(\cos^{2}(t))dt
sum from n=2 to infinity of sin(1/n)	\sum\:_{n=2}^{\infty\:}\sin(\frac{1}{n})
integral from-pi to pi of x^2cos(2x)	\int\:_{-π}^{π}x^{2}\cos(2x)dx

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