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Popular Calculus Problems

integral from 0 to 4 of 1/(x^2-6x+5)	\int\:_{0}^{4}\frac{1}{x^{2}-6x+5}dx
(e^{-3x})^'	(e^{-3x})^{\prime\:}
derivative of ln((x+1/(x^3+1)))	\frac{d}{dx}(\ln(\frac{x+1}{x^{3}+1}))
derivative of (-16x^2+36)^2	derivative\:(-16x^{2}+36)^{2}
derivative of cos(3x^2+x-1)	\frac{d}{dx}(\cos(3x^{2}+x-1))
derivative of ln(x+(x-1)/x)	\frac{d}{dx}(\ln(x)+\frac{x-1}{x})
integral of cos(-3x)	\int\:\cos(-3x)dx
tangent of xy^3+5xy=36,(6,1)	tangent\:xy^{3}+5xy=36,(6,1)
(\partial)/(\partial x)(3exsin(y))	\frac{\partial\:}{\partial\:x}(3ex\sin(y))
integral of (x^3+2)	\int\:(x^{3}+2)dx
integral of-(sin^2(x))/(cos(x))	\int\:-\frac{\sin^{2}(x)}{\cos(x)}dx
derivative of (x^2+3/(x^2-1))	\frac{d}{dx}(\frac{x^{2}+3}{x^{2}-1})
derivative of (sin(4t))/(cos(6t))	derivative\:\frac{\sin(4t)}{\cos(6t)}
derivative of y=sqrt(x)^{3x}	derivative\:y=\sqrt{x}^{3x}
y^{''}+y=sec(t)	y^{\prime\:\prime\:}+y=\sec(t)
sum from n=1 to infinity of (6n)/(9-2n)	\sum\:_{n=1}^{\infty\:}\frac{6n}{9-2n}
maclaurin f(x)=(1+x)^{-5/3}	maclaurin\:f(x)=(1+x)^{-\frac{5}{3}}
integral of x^2(6x^3-5)^4	\int\:x^{2}(6x^{3}-5)^{4}dx
limit as x approaches 0 of (3^x)/(3^x-1)	\lim\:_{x\to\:0}(\frac{3^{x}}{3^{x}-1})
integral of arccot(4x)	\int\:\arccot(4x)dx
integral of (3x+10)^{12}	\int\:(3x+10)^{12}dx
integral of (1+y^2)^{-3/2}	\int\:(1+y^{2})^{-\frac{3}{2}}dy
integral from-infinity to 3 of 3/(x^2+9)	\int\:_{-\infty\:}^{3}\frac{3}{x^{2}+9}dx
area f(x)=x+2,x=1,x=3	area\:f(x)=x+2,x=1,x=3
y^'=(x-y)/(x+2y)	y^{\prime\:}=\frac{x-y}{x+2y}
(d^2)/(dx^2)(x/(4-6x))	\frac{d^{2}}{dx^{2}}(\frac{x}{4-6x})
derivative of t^2+2sqrt(t)+50	derivative\:t^{2}+2\sqrt{t}+50
derivative of sqrt(t)(a+bt)	\frac{d}{dx}(\sqrt{t}(a+bt))
y^{''}+3y^'+2y= 1/(4+e^x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\frac{1}{4+e^{x}}
limit as x approaches 2+of e^{(3/(2-x))}	\lim\:_{x\to\:2+}(e^{(\frac{3}{2-x})})
derivative of (3+2x/(5-8x))	\frac{d}{dx}(\frac{3+2x}{5-8x})
derivative of 3cos(x-cos(3x))	\frac{d}{dx}(3\cos(x)-\cos(3x))
derivative of x^{2pi}	\frac{d}{dx}(x^{2π})
integral of (2cos(x/2)-3cos(x/3))^2	\int\:(2\cos(\frac{x}{2})-3\cos(\frac{x}{3}))^{2}dx
derivative of 5/(x^2-2)	\frac{d}{dx}(\frac{5}{x^{2}-2})
integral of v^{-2}(2v^4+3v^2-2v^{-3})	\int\:v^{-2}(2v^{4}+3v^{2}-2v^{-3})dv
(\partial)/(\partial x)(x^3+e^{y^2})	\frac{\partial\:}{\partial\:x}(x^{3}+e^{y^{2}})
y^'+y=sin(x)	y^{\prime\:}+y=\sin(x)
limit as x approaches 5 of ln(x/5)	\lim\:_{x\to\:5}(\ln(\frac{x}{5}))
sum from n=1 to infinity of sqrt(n)	\sum\:_{n=1}^{\infty\:}\sqrt{n}
derivative of f(x)=ln(4x)	derivative\:f(x)=\ln(4x)
y^{''}+y^'+5y=0,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y^{\prime\:}+5y=0,y(0)=0,y^{\prime\:}(0)=0
limit as h approaches 0 of (2^h-1)/h	\lim\:_{h\to\:0}(\frac{2^{h}-1}{h})
derivative of x^{sqrt(6)}	\frac{d}{dx}(x^{\sqrt{6}})
limit as x approaches 4 of+(2sqrt(x-4))	\lim\:_{x\to\:4}(+(2\sqrt{x-4}))
v(dv)/(dy)+v^2=2e^{-y}	v\frac{dv}{dy}+v^{2}=2e^{-y}
derivative of ((x^2-2)/x)	\frac{d}{dx}(\frac{(x^{2}-2)}{x})
derivative of (1-3x^2^{1/(sin^2(x))})	\frac{d}{dx}((1-3x^{2})^{\frac{1}{\sin^{2}(x)}})
integral of [xsqrt((x-1))]	\int\:[x\sqrt{(x-1)}]dx
limit as x approaches 1+of 4/(x^3-1)	\lim\:_{x\to\:1+}(\frac{4}{x^{3}-1})
integral of 3x^2(x^3+4)^4	\int\:3x^{2}(x^{3}+4)^{4}dx
f(x)=ln(sin(2x))	f(x)=\ln(\sin(2x))
area y=5x^2,y=30x-45,[0,3]	area\:y=5x^{2},y=30x-45,[0,3]
(dy)/(dt)+3/t y=3t^2y^2	\frac{dy}{dt}+\frac{3}{t}y=3t^{2}y^{2}
inverse oflaplace (5s)/((s^2+1)^2)	inverselaplace\:\frac{5s}{(s^{2}+1)^{2}}
derivative of 5x^2-sin(pix)	derivative\:5x^{2}-\sin(πx)
y^'+4y=e^{-4t},y(0)=2	y^{\prime\:}+4y=e^{-4t},y(0)=2
derivative of y=(3+csc(x))/(7-csc(x))	derivative\:y=\frac{3+\csc(x)}{7-\csc(x)}
tangent of (2x)/((x^2-5)^3),\at x=0	tangent\:\frac{2x}{(x^{2}-5)^{3}},\at\:x=0
integral of 1/(x^3sqrt(x^2-81))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-81}}dx
integral of 3\sqrt[5]{x}	\int\:3\sqrt[5]{x}dx
derivative of (3x-1(x-2)^4)	\frac{d}{dx}((3x-1)(x-2)^{4})
(dy)/(dx)(1+x)-xy=x+x^2	\frac{dy}{dx}(1+x)-xy=x+x^{2}
derivative of y=2xsin(x)	derivative\:y=2x\sin(x)
limit as x approaches 0 of (4x)/(\|x\|)	\lim\:_{x\to\:0}(\frac{4x}{\left\|x\right\|})
y^{''}-8y^'=5t	y^{\prime\:\prime\:}-8y^{\prime\:}=5t
y^{''}+4y^'+4y=12t+16,y(0)=3,y^'(0)=-4	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=12t+16,y(0)=3,y^{\prime\:}(0)=-4
derivative of (2^0/(3^1+0))	\frac{d}{dx}(\frac{2^{0}}{3^{1}+0})
limit as n approaches infinity of n	\lim\:_{n\to\:\infty\:}(n)
y^'-2y=0,y(0)=2	y^{\prime\:}-2y=0,y(0)=2
derivative of f(x)=cos(sin(5)x^3)	derivative\:f(x)=\cos(\sin(5)x^{3})
(\partial)/(\partial x)(9x^6y^5+6x^8y^4)	\frac{\partial\:}{\partial\:x}(9x^{6}y^{5}+6x^{8}y^{4})
y^'+y=e^{6t}	y^{\prime\:}+y=e^{6t}
derivative of ln(x+sqrt(x^2+4))	derivative\:\ln(x+\sqrt{x^{2}+4})
(3x+2y+1)dx-(3x+2y-1)dy=0	(3x+2y+1)\cdot\:dx-(3x+2y-1)\cdot\:dy=0
integral of (2x^4+3x^3-x)/(x^3)	\int\:\frac{2x^{4}+3x^{3}-x}{x^{3}}dx
tangent of f(x)=sqrt(x+7),\at x=-6	tangent\:f(x)=\sqrt{x+7},\at\:x=-6
derivative of 4^{-x/4}	\frac{d}{dx}(4^{-\frac{x}{4}})
derivative of (4x^2-3)/(8x^3+1)	derivative\:\frac{4x^{2}-3}{8x^{3}+1}
derivative of (xcos(pix+1)/(1-x))	\frac{d}{dx}(\frac{x\cos(πx)+1}{1-x})
inverse oflaplace (s+1)/(s^2+2)	inverselaplace\:\frac{s+1}{s^{2}+2}
(y-x2)dx+(x+y2)dy=0	(y-x2)dx+(x+y2)dy=0
integral of ((-4)/x)	\int\:(\frac{-4}{x})dx
integral of 1/n sin(nx)	\int\:\frac{1}{n}\sin(nx)dx
inverse oflaplace (104)/(s^2+8s+52)	inverselaplace\:\frac{104}{s^{2}+8s+52}
derivative of (x^3-7/(x^2+2))	\frac{d}{dx}(\frac{x^{3}-7}{x^{2}+2})
integral of 1/(7\sqrt[7]{x^6)}	\int\:\frac{1}{7\sqrt[7]{x^{6}}}dx
(d^3)/(dx^3)(1/(1-x))	\frac{d^{3}}{dx^{3}}(\frac{1}{1-x})
derivative of 3x^2+2x-4	\frac{d}{dx}(3x^{2}+2x-4)
integral of x/((4+x^2))	\int\:\frac{x}{(4+x^{2})}dx
integral of ((3t-2))/(t+1)	\int\:\frac{(3t-2)}{t+1}dt
derivative of 3/(x^5)	derivative\:\frac{3}{x^{5}}
y^'+5y=15	y^{\prime\:}+5y=15
(\partial)/(\partial x)(-x-sin(y^2))	\frac{\partial\:}{\partial\:x}(-x-\sin(y^{2}))
integral of x(cos(x)-sin(x))	\int\:x(\cos(x)-\sin(x))dx
derivative of x-0.8-0.2*sin(x)	\frac{d}{dx}(x-0.8-0.2\cdot\:\sin(x))
derivative of-((2x^2+1)/((1-x^2)^{5/2)})	\frac{d}{dx}(-\frac{(2x^{2}+1)}{(1-x^{2})^{\frac{5}{2}}})
x(dy)/(dx)=y^2	x\frac{dy}{dx}=y^{2}
taylor sin(4x)	taylor\:\sin(4x)
integral of-(e^{4x})/(4x)	\int\:-\frac{e^{4x}}{4x}dx

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