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Popular Calculus Problems

limit as x approaches 0 of-cos(x)+1	\lim\:_{x\to\:0}(-\cos(x)+1)
integral of (5x^2)/(x+1)	\int\:\frac{5x^{2}}{x+1}dx
y=x(1-x)^6	y=x(1-x)^{6}
inverse oflaplace f(s)=s-3(s^2+4s+13)	inverselaplace\:f(s)=s-3(s^{2}+4s+13)
area y^2=4x,y^2= 4/x	area\:y^{2}=4x,y^{2}=\frac{4}{x}
sum from n=1 to infinity of ((2n)!)/(5^n(n!)^2)	\sum\:_{n=1}^{\infty\:}\frac{(2n)!}{5^{n}(n!)^{2}}
limit as x approaches 0 of (e^{x^5}-1)/x	\lim\:_{x\to\:0}(\frac{e^{x^{5}}-1}{x})
(\partial)/(\partial x)(sqrt((x+3)/(y+2)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+3}{y+2}})
integral from 2 to r of 1/(xln(x))	\int\:_{2}^{r}\frac{1}{x\ln(x)}dx
integral of (e^x)/((4-e^x)^2)	\int\:\frac{e^{x}}{(4-e^{x})^{2}}dx
integral of (3x+6)/(sqrt(2x^2+8x+3))	\int\:\frac{3x+6}{\sqrt{2x^{2}+8x+3}}dx
limit as x approaches pi/4 of 2cot(2x)	\lim\:_{x\to\:\frac{π}{4}}(2\cot(2x))
integral of (x/(x+2))	\int\:(\frac{x}{x+2})dx
limit as x approaches 7 of (x-8)/(x-7)	\lim\:_{x\to\:7}(\frac{x-8}{x-7})
y^{''}=y-3x	y^{\prime\:\prime\:}=y-3x
derivative of 5/3 x^3-x^2+1	\frac{d}{dx}(\frac{5}{3}x^{3}-x^{2}+1)
limit as x approaches-1 of 4x^3-2x^2+2	\lim\:_{x\to\:-1}(4x^{3}-2x^{2}+2)
derivative of f(x)=x^2-sqrt(x+4)	derivative\:f(x)=x^{2}-\sqrt{x+4}
d/(dt)(cot^4(t)-csc^4(t))	\frac{d}{dt}(\cot^{4}(t)-\csc^{4}(t))
limit as x approaches 4 of 8-2x	\lim\:_{x\to\:4}(8-2x)
limit as x approaches infinity of 8^x	\lim\:_{x\to\:\infty\:}(8^{x})
integral of 8x^2e^x	\int\:8x^{2}e^{x}dx
derivative of 2(x+4)^{3/2}	derivative\:2(x+4)^{\frac{3}{2}}
(\partial)/(\partial x)(y^2+x^2-4x-3)	\frac{\partial\:}{\partial\:x}(y^{2}+x^{2}-4x-3)
(\partial)/(\partial x)(e^{xz+2}-cos(x+y))	\frac{\partial\:}{\partial\:x}(e^{xz+2}-\cos(x+y))
derivative of ((e^x))/((e^x+4)(x+5))	derivative\:\frac{(e^{x})}{(e^{x}+4)(x+5)}
csc(y)dx+sec(2)(x)dy=0	\csc(y)dx+\sec(2)(x)dy=0
(d^2}{dx^2}(\frac{6x^5)/5-7x)	\frac{d^{2}}{dx^{2}}(\frac{6x^{5}}{5}-7x)
integral of (sin(y)cos(x))	\int\:(\sin(y)\cos(x))dx
y^'=y^2e^{(2x)}	y^{\prime\:}=y^{2}e^{(2x)}
derivative of 4^xln(x)	\frac{d}{dx}(4^{x}\ln(x))
derivative of f(x)=5cos^2(pix)	derivative\:f(x)=5\cos^{2}(πx)
integral of 6(e^{2x})/8	\int\:6\frac{e^{2x}}{8}dx
integral of xe^{-x/2}	\int\:xe^{-\frac{x}{2}}dx
integral of (10)/(1+4x^2)	\int\:\frac{10}{1+4x^{2}}dx
integral of (x^2+6)/(x^3+x)	\int\:\frac{x^{2}+6}{x^{3}+x}dx
derivative of 5/((2x-3^4))	\frac{d}{dx}(\frac{5}{(2x-3)^{4}})
slope ofintercept (0,5),(10,0)	slopeintercept\:(0,5),(10,0)
(\partial)/(\partial x)(e^{5xyz-3})	\frac{\partial\:}{\partial\:x}(e^{5xyz-3})
integral of (1/(sqrt(y+4)-2))	\int\:(\frac{1}{\sqrt{y+4}-2})dy
integral of-pisin(pi)x	\int\:-π\sin(π)xdx
limit as x approaches 0 of e^{6x}	\lim\:_{x\to\:0}(e^{6x})
(\partial)/(\partial y)(sin(pi(x-y)))	\frac{\partial\:}{\partial\:y}(\sin(π(x-y)))
y^'=5y+y^5	y^{\prime\:}=5y+y^{5}
derivative of (x^2/(3x+7))	\frac{d}{dx}(\frac{x^{2}}{3x+7})
derivative of y= 1/(f(x))	derivative\:y=\frac{1}{f(x)}
derivative of x^{1/3}-1	derivative\:x^{\frac{1}{3}}-1
d/(dt)(1/((t+1)^2))	\frac{d}{dt}(\frac{1}{(t+1)^{2}})
integral of 3xy^2	\int\:3xy^{2}dy
(\partial)/(\partial x)(e^{e^y(1+e^x)-2})	\frac{\partial\:}{\partial\:x}(e^{e^{y}(1+e^{x})-2})
area x^2-2,-(x-1)^2+3	area\:x^{2}-2,-(x-1)^{2}+3
integral of x^4(3x^5-1)^6	\int\:x^{4}(3x^{5}-1)^{6}dx
xdy-ydx=sqrt(x^2+y^2)dx	xdy-ydx=\sqrt{x^{2}+y^{2}}dx
(dy)/(dx)=5^xln(5)+1/(x^2+1)	\frac{dy}{dx}=5^{x}\ln(5)+\frac{1}{x^{2}+1}
derivative of sin(23x)	\frac{d}{dx}(\sin(23x))
derivative of (x^3+2x^2-4/3)	\frac{d}{dx}(\frac{x^{3}+2x^{2}-4}{3})
integral of csc^{15}(x)	\int\:\csc^{15}(x)dx
integral from 1 to 5 of 4/(x^2+2x+1)	\int\:_{1}^{5}\frac{4}{x^{2}+2x+1}dx
integral of (sin(x))/(cos^3(x))	\int\:\frac{\sin(x)}{\cos^{3}(x)}dx
derivative of-1/((1-x^2))	\frac{d}{dx}(-\frac{1}{(1-x)^{2}})
derivative of y=arctan(sqrt(4t))	derivative\:y=\arctan(\sqrt{4t})
limit as x approaches 2+of (4x)/(x-2)	\lim\:_{x\to\:2+}(\frac{4x}{x-2})
xy^'-2y=x^2-2x-1	xy^{\prime\:}-2y=x^{2}-2x-1
(\partial)/(\partial x)(cot(xy))	\frac{\partial\:}{\partial\:x}(\cot(xy))
taylor 1/((1-x)),2	taylor\:\frac{1}{(1-x)},2
integral of (x^2-19)/(x^3-2x^2+x)	\int\:\frac{x^{2}-19}{x^{3}-2x^{2}+x}dx
integral of 0.2x	\int\:0.2xdx
(dx)/(dt)=(7x^2+3tsqrt(8t^2+x^2))/(7tx)	\frac{dx}{dt}=\frac{7x^{2}+3t\sqrt{8t^{2}+x^{2}}}{7tx}
integral of sqrt(t)*ln(t)	\int\:\sqrt{t}\cdot\:\ln(t)dt
derivative of y=(4x^2+5)(3x-5)	derivative\:y=(4x^{2}+5)(3x-5)
tangent of 2x^3-3x^2-72x+2	tangent\:2x^{3}-3x^{2}-72x+2
inverse oflaplace (s+1)/(s^2-4s)	inverselaplace\:\frac{s+1}{s^{2}-4s}
derivative of 2*e^{x^2-4x}	derivative\:2\cdot\:e^{x^{2}-4x}
integral of 2x-5	\int\:2x-5dx
integral of 8xln(3x)	\int\:8x\ln(3x)dx
derivative of xln(x^2+4+4arctan(x/2)-2x)	\frac{d}{dx}(x\ln(x^{2}+4)+4\arctan(\frac{x}{2})-2x)
integral of arctan(2y)	\int\:\arctan(2y)dy
derivative of cos(sqrt(3x))	\frac{d}{dx}(\cos(\sqrt{3x}))
integral of x+2y	\int\:x+2ydy
integral of sin(x)cos(x)e^{sin(x)}	\int\:\sin(x)\cos(x)e^{\sin(x)}dx
sum from n=0 to infinity of (5n)/(n^2+4)	\sum\:_{n=0}^{\infty\:}\frac{5n}{n^{2}+4}
f(x)=(e^x)/(ln(x))	f(x)=\frac{e^{x}}{\ln(x)}
integral of 1/((2+cos(x)))	\int\:\frac{1}{(2+\cos(x))}dx
laplacetransform (t-5)^3	laplacetransform\:(t-5)^{3}
derivative of (5x^2/2)	\frac{d}{dx}(\frac{5x^{2}}{2})
(y)dx-4(x+y^6)dy=0	(y)dx-4(x+y^{6})dy=0
tangent of f(x)=3-4x^2,(4,-61)	tangent\:f(x)=3-4x^{2},(4,-61)
derivative of 5cos(t)	derivative\:5\cos(t)
derivative of 3e^xsin(x)	\frac{d}{dx}(3e^{x}\sin(x))
y^{''}+16y=-16sec^2(4x)	y^{\prime\:\prime\:}+16y=-16\sec^{2}(4x)
(\partial)/(\partial x)((c+1)/(c+x))	\frac{\partial\:}{\partial\:x}(\frac{c+1}{c+x})
derivative of (x-3/(x+2))	\frac{d}{dx}(\frac{x-3}{x+2})
(dy)/(dx)=3xsqrt(y)	\frac{dy}{dx}=3x\sqrt{y}
f(x)=arccos(x^2)	f(x)=\arccos(x^{2})
slope of (0,-2),(1,2)	slope\:(0,-2),(1,2)
(\partial)/(\partial u)(1/3 (v-2u))	\frac{\partial\:}{\partial\:u}(\frac{1}{3}(v-2u))
(\partial)/(\partial x)(-ycos(6x))	\frac{\partial\:}{\partial\:x}(-y\cos(6x))
limit as x approaches 0 of-2x-h+4	\lim\:_{x\to\:0}(-2x-h+4)
sum from n=1 to infinity}(-1)^{n+1 of (3/(2^n))	\sum\:_{n=1}^{\infty\:}(-1)^{n+1}(\frac{3}{2^{n}})
integral of 1/(sin(2y)cos(2y))	\int\:\frac{1}{\sin(2y)\cos(2y)}dy

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