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Popular Calculus Problems

f(x)= 1/(x^2-5)	f(x)=\frac{1}{x^{2}-5}
integral of sin(22x)sin(23x)	\int\:\sin(22x)\sin(23x)dx
integral of (-1)/t	\int\:\frac{-1}{t}dt
limit as x approaches 1+of x^{x/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{x}{1-x}})
x^2(dy)/(dx)=y-xy,y(-1)=-4	x^{2}\frac{dy}{dx}=y-xy,y(-1)=-4
derivative of pi/((2x)^5)	derivative\:\frac{π}{(2x)^{5}}
simplify 2sin(x)cos(x)	simplify\:2\sin(x)\cos(x)
derivative of sqrt(2x^2-1)	derivative\:\sqrt{2x^{2}-1}
limit as x approaches 1-of ln(x-1)	\lim\:_{x\to\:1-}(\ln(x-1))
derivative of 9/((x-6^{4/3)})	\frac{d}{dx}(\frac{9}{(x-6)^{\frac{4}{3}}})
integral of 10sqrt(5x^2-1)	\int\:10\sqrt{5x^{2}-1}dx
y^{''}+6y^'+9y=e^{2x}(3-5x)	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=e^{2x}(3-5x)
integral of (x+4)/(2x^2+x-1)	\int\:\frac{x+4}{2x^{2}+x-1}dx
tangent of f(x)=sqrt(x+15),\at x=1	tangent\:f(x)=\sqrt{x+15},\at\:x=1
(3x^2)dx+(2y-4x^3y^{-1})dy=0	(3x^{2})dx+(2y-4x^{3}y^{-1})dy=0
integral of xsin^2(5x)	\int\:x\sin^{2}(5x)dx
(dy)/(dt)=1y	\frac{dy}{dt}=1y
integral of (x+2)/(sqrt(x+1))	\int\:\frac{x+2}{\sqrt{x+1}}dx
maclaurin 11cos(-x)	maclaurin\:11\cos(-x)
derivative of 3sin(x-sin(3x))	\frac{d}{dx}(3\sin(x)-\sin(3x))
limit as x approaches+0 of (-1)/(5x)	\lim\:_{x\to\:+0}(\frac{-1}{5x})
(\partial)/(\partial t)(x/t-2t)	\frac{\partial\:}{\partial\:t}(\frac{x}{t}-2t)
derivative of (sin(x)^{sin(x)})	\frac{d}{dx}((\sin(x))^{\sin(x)})
derivative of (3x^2+6^3)	\frac{d}{dx}((3x^{2}+6)^{3})
derivative of f(x)=ln(sqrt(x)+1)	derivative\:f(x)=\ln(\sqrt{x}+1)
limit as x approaches infinity of-3x^4	\lim\:_{x\to\:\infty\:}(-3x^{4})
integral of tan^2(xse)c^{10}x	\int\:\tan^{2}(xse)c^{10}xdx
integral of 2sqrt(1-e^{-x)}e^{-x}	\int\:2\sqrt{1-e^{-x}}e^{-x}dx
laplacetransform-5cos(0.4t)	laplacetransform\:-5\cos(0.4t)
y^'=y^2	y^{\prime\:}=y^{2}
integral of u*e^u	\int\:u\cdot\:e^{u}du
x(dy)/(dx)=y+x^2sin(x)	x\frac{dy}{dx}=y+x^{2}\sin(x)
integral of 7sqrt(t)	\int\:7\sqrt{t}dt
integral of 8tan^2(x)	\int\:8\tan^{2}(x)dx
integral of 1/((x+2)(x+4))	\int\:\frac{1}{(x+2)(x+4)}dx
(1+xy)dx+x^2dy=0	(1+xy)dx+x^{2}dy=0
integral of-sin(x)tan(x)	\int\:-\sin(x)\tan(x)dx
inverse oflaplace 1/((s+2)^2+1)	inverselaplace\:\frac{1}{(s+2)^{2}+1}
derivative of (8-xe^x)/(x+e^x)	derivative\:\frac{8-xe^{x}}{x+e^{x}}
integral of (x+x^3)/x-e^x	\int\:\frac{x+x^{3}}{x}-e^{x}dx
f(x)=(e^x-e^{-x})/2	f(x)=\frac{e^{x}-e^{-x}}{2}
integral of x^3e^{3x}	\int\:x^{3}e^{3x}dx
integral of 2t+4	\int\:2t+4dt
inverse oflaplace (2s+3)/(s^2-7)	inverselaplace\:\frac{2s+3}{s^{2}-7}
tangent of y=5+5x^2-2x^3,\at x=a	tangent\:y=5+5x^{2}-2x^{3},\at\:x=a
(dy)/(dx)=(4sec(y))/((x+6)^2)	\frac{dy}{dx}=\frac{4\sec(y)}{(x+6)^{2}}
derivative of (e^x/(2x^2+5))	\frac{d}{dx}(\frac{e^{x}}{2x^{2}+5})
integral from-1 to 1 of 2	\int\:_{-1}^{1}2dx
limit as b approaches 0 of b/(x^2+b^2)	\lim\:_{b\to\:0}(\frac{b}{x^{2}+b^{2}})
sum from n=3 to infinity of (4^n+1)/(n!)	\sum\:_{n=3}^{\infty\:}\frac{4^{n}+1}{n!}
derivative of y= 1/((1+x^2))	derivative\:y=\frac{1}{(1+x^{2})}
simplify 3x^{-2}-4x	simplify\:3x^{-2}-4x
derivative of e^{1+(ln(x))^2}	derivative\:e^{1+(\ln(x))^{2}}
sqrt(1-y^2)dx-sqrt(1-x^2)dy=0,y(0)= 1/2	\sqrt{1-y^{2}}dx-\sqrt{1-x^{2}}dy=0,y(0)=\frac{1}{2}
y^'=e^{t-y}	y^{\prime\:}=e^{t-y}
integral of (3x-11)e^x	\int\:(3x-11)e^{x}dx
3y^{''}-7y^'+2y=0,y(0)=-3,y^'(0)=-8	3y^{\prime\:\prime\:}-7y^{\prime\:}+2y=0,y(0)=-3,y^{\prime\:}(0)=-8
integral of sin(x)-8cos(x)	\int\:\sin(x)-8\cos(x)dx
derivative of f(x)=cot(7x)	derivative\:f(x)=\cot(7x)
limit as x approaches 0 of ((1/((x+4)))-(1/4))/x	\lim\:_{x\to\:0}(\frac{(\frac{1}{(x+4)})-(\frac{1}{4})}{x})
derivative of sqrt(5x+8)	derivative\:\sqrt{5x+8}
y^'= x/(1+x^2)	y^{\prime\:}=\frac{x}{1+x^{2}}
derivative of ((x+1^3)/x)	\frac{d}{dx}(\frac{(x+1)^{3}}{x})
y^'=y^2-(xy)^2	y^{\prime\:}=y^{2}-(xy)^{2}
integral of 1/(3sqrt(x)(2+\sqrt{x))}	\int\:\frac{1}{3\sqrt{x}(2+\sqrt{x})}dx
limit as x approaches 2-of arcsin(x/2)	\lim\:_{x\to\:2-}(\arcsin(\frac{x}{2}))
limit as x approaches-1 of (x+2x^4)^3	\lim\:_{x\to\:-1}((x+2x^{4})^{3})
integral of y^x	\int\:y^{x}dx
integral of (cos^4(x))/(sin^7(x))	\int\:\frac{\cos^{4}(x)}{\sin^{7}(x)}dx
(1+x)y^'+y=cos(x)	(1+x)y^{\prime\:}+y=\cos(x)
(\partial)/(\partial x)(e^xsin(3y))	\frac{\partial\:}{\partial\:x}(e^{x}\sin(3y))
sum from n=1 to infinity of 2/(n!)	\sum\:_{n=1}^{\infty\:}\frac{2}{n!}
integral of 5^3	\int\:5^{3}dx
derivative of xg(x)	derivative\:xg(x)
(\partial)/(\partial x)(xe^{xy}+y)	\frac{\partial\:}{\partial\:x}(xe^{xy}+y)
integral of 3/(2x)	\int\:\frac{3}{2x}dx
(dy)/(dx)=(xe^{3x+y^3})/(y^2)	\frac{dy}{dx}=\frac{xe^{3x+y^{3}}}{y^{2}}
derivative of (3x^3-4(-4x-3))	\frac{d}{dx}((3x^{3}-4)(-4x-3))
4x^2y^'=y^'+9xe^{-y}	4x^{2}y^{\prime\:}=y^{\prime\:}+9xe^{-y}
integral of 1x	\int\:1xdx
derivative of y=19sin(x)cos(x)	derivative\:y=19\sin(x)\cos(x)
derivative of tan(ln(ax+b))	derivative\:\tan(\ln(ax+b))
area y=6-3x^2,y=3x^2,x=-2,x=2	area\:y=6-3x^{2},y=3x^{2},x=-2,x=2
area f(x)=-x^3+8,-8,1	area\:f(x)=-x^{3}+8,-8,1
integral of-x^2-x	\int\:-x^{2}-xdx
integral of (ln(y^3))/(8y)	\int\:\frac{\ln(y^{3})}{8y}dy
tangent of f(x)=x^2+3x-1,\at x=-1	tangent\:f(x)=x^{2}+3x-1,\at\:x=-1
integral of 1/(xsqrt(9x^2-49))	\int\:\frac{1}{x\sqrt{9x^{2}-49}}dx
derivative of 1/((1+x^3))	\frac{d}{dx}(\frac{1}{(1+x)^{3}})
4y^{''}+16y^'+19y=0	4y^{\prime\:\prime\:}+16y^{\prime\:}+19y=0
derivative of arctan(d/x)	\frac{d}{dx}(\arctan(\frac{d}{x}))
y^{''}+2y^'=(8t-7)sin(3t)	y^{\prime\:\prime\:}+2y^{\prime\:}=(8t-7)\sin(3t)
integral of e^{2t}	\int\:e^{2t}dt
(\partial)/(\partial y)(x^3cos(y))	\frac{\partial\:}{\partial\:y}(x^{3}\cos(y))
limit as x approaches 0 of 5x^2	\lim\:_{x\to\:0}(5x^{2})
y(dy)/(dx)=x	y\frac{dy}{dx}=x
slope of (3,6),(5,8)	slope\:(3,6),(5,8)
integral of sec^5(x)tan^5(x)	\int\:\sec^{5}(x)\tan^{5}(x)dx
integral of (25)/(x^3-5x^2)	\int\:\frac{25}{x^{3}-5x^{2}}dx
integral of 1+x+e^x	\int\:1+x+e^{x}dx

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