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Popular Calculus Problems

limit as x approaches 0 of ln(x/3)+x^2-8	\lim\:_{x\to\:0}(\ln(\frac{x}{3})+x^{2}-8)
laplacetransform 2/3 t^3e^{-8t}	laplacetransform\:\frac{2}{3}t^{3}e^{-8t}
derivative of 3cos(x-sin(x))	\frac{d}{dx}(3\cos(x)-\sin(x))
(dy)/(dx)+2xy-y=0,y(0)=4	\frac{dy}{dx}+2xy-y=0,y(0)=4
integral of (x+9)/(sqrt(16-(x-4)^2))	\int\:\frac{x+9}{\sqrt{16-(x-4)^{2}}}dx
integral of (sin(x))^{11}(cos(x))^5	\int\:(\sin(x))^{11}(\cos(x))^{5}dx
y^'=y^3-6x^2y^3,y(1)=-1/2	y^{\prime\:}=y^{3}-6x^{2}y^{3},y(1)=-\frac{1}{2}
limit as x approaches 1 of (x^2+1)/(x+1)	\lim\:_{x\to\:1}(\frac{x^{2}+1}{x+1})
derivative of f(x)=80640(2x+5)^2	derivative\:f(x)=80640(2x+5)^{2}
tangent of f(x)=x^2-x	tangent\:f(x)=x^{2}-x
derivative of 2xsqrt(x)	derivative\:2x\sqrt{x}
tangent of y=x+tan(x),(pi,pi)	tangent\:y=x+\tan(x),(π,π)
limit as x approaches 0 of ln(sinh(x))	\lim\:_{x\to\:0}(\ln(\sinh(x)))
integral of 4/369 x^3	\int\:\frac{4}{369}x^{3}dx
limit as x approaches 1 of sqrt(3x^2+4)	\lim\:_{x\to\:1}(\sqrt{3x^{2}+4})
area y=x^2-8,y=8	area\:y=x^{2}-8,y=8
derivative of sin(pi^2)	\frac{d}{dx}(\sin(π^{2}))
(e^{-x/2})^'	(e^{-\frac{x}{2}})^{\prime\:}
y^'-y=1,y(0)=1	y^{\prime\:}-y=1,y(0)=1
integral of sin^3(18x)cos^3(18x)	\int\:\sin^{3}(18x)\cos^{3}(18x)dx
integral of (8x)/((1-x^2)^4)	\int\:\frac{8x}{(1-x^{2})^{4}}dx
(\partial)/(\partial z)((4x-4z)/(y+4z))	\frac{\partial\:}{\partial\:z}(\frac{4x-4z}{y+4z})
yy^'=x-2x^3	yy^{\prime\:}=x-2x^{3}
derivative of a^7+(cos(x)^7)	\frac{d}{dx}(a^{7}+(\cos(x))^{7})
area x=y^2+4y-22,x=3y+8	area\:x=y^{2}+4y-22,x=3y+8
derivative of x-tan(x)	derivative\:x-\tan(x)
x(x+y)(dy)/(dx)=y(x-y)	x(x+y)\frac{dy}{dx}=y(x-y)
derivative of sqrt(4x+9)	derivative\:\sqrt{4x+9}
sum from n=1 to infinity of 8-7(0.8)^n	\sum\:_{n=1}^{\infty\:}8-7(0.8)^{n}
limit as x approaches 17 of 3x+2	\lim\:_{x\to\:17}(3x+2)
y=(3x^2+5)^4	y=(3x^{2}+5)^{4}
y^'+xe^{(-x^2)/2}=0	y^{\prime\:}+xe^{\frac{-x^{2}}{2}}=0
derivative of sqrt(x)+sqrt(y)=4	\frac{d}{dx}(\sqrt{x}+\sqrt{y})=4
(dy)/(dx)=e^{y-2x}	\frac{dy}{dx}=e^{y-2x}
integral of 20sin^2(x)cos^2(x)	\int\:20\sin^{2}(x)\cos^{2}(x)dx
integral of (5^{3x})/(5^{3x)+7}	\int\:\frac{5^{3x}}{5^{3x}+7}dx
slope of-3x^2+4p+4	slope\:-3x^{2}+4p+4
(d^3)/(dx^3)(sin(2x))	\frac{d^{3}}{dx^{3}}(\sin(2x))
area x^2-4x,0	area\:x^{2}-4x,0
derivative of (2(16-x^2)/((16+x^2)^2))	\frac{d}{dx}(\frac{2(16-x^{2})}{(16+x^{2})^{2}})
integral of (cos(x)+sin(x))	\int\:(\cos(x)+\sin(x))dx
derivative of asin(5x)	\frac{d}{dx}(a\sin(5x))
limit as x approaches-3 of (x^2)/(x^2-9)	\lim\:_{x\to\:-3}(\frac{x^{2}}{x^{2}-9})
(\partial)/(\partial x)(xsin(x^2-y^2))	\frac{\partial\:}{\partial\:x}(x\sin(x^{2}-y^{2}))
(x+ye^{y/x})dx-(xe^{y/x})dy=0	(x+ye^{\frac{y}{x}})dx-(xe^{\frac{y}{x}})dy=0
derivative of (-x^2-5/((x^2-5)^2))	\frac{d}{dx}(\frac{-x^{2}-5}{(x^{2}-5)^{2}})
integral of e^{2x}-xe^{2x}	\int\:e^{2x}-xe^{2x}dx
derivative of-7csc(x+1/(x^5))	\frac{d}{dx}(-7\csc(x)+\frac{1}{x^{5}})
derivative of arcsin(x/a)	derivative\:\arcsin(\frac{x}{a})
derivative of (4/3)pix^3	derivative\:(\frac{4}{3})πx^{3}
derivative of 4xy^2-x^2y^2-xy^3	\frac{d}{dx}(4xy^{2}-x^{2}y^{2}-xy^{3})
integral of-1/2 x^{1/2}	\int\:-\frac{1}{2}x^{\frac{1}{2}}dx
tangent of f(x)=-3x^2+3x+1,\at x=1	tangent\:f(x)=-3x^{2}+3x+1,\at\:x=1
derivative of y= 2/(1-9x^2)	derivative\:y=\frac{2}{1-9x^{2}}
integral from 0 to pi/2 of xcos(x/3)	\int\:_{0}^{\frac{π}{2}}x\cos(\frac{x}{3})dx
derivative of (2ln(x))/x	derivative\:\frac{2\ln(x)}{x}
(dy)/(dx)=2y(9-y)	\frac{dy}{dx}=2y(9-y)
(dx)/(dt)=x(1-1/2500 x)	\frac{dx}{dt}=x(1-\frac{1}{2500}x)
integral of (x+4)sqrt(8x+x^2)	\int\:(x+4)\sqrt{8x+x^{2}}dx
derivative of sqrt(r^2-7x^2)	\frac{d}{dx}(\sqrt{r^{2}-7x^{2}})
derivative of 2sec^2(xtan(x))	\frac{d}{dx}(2\sec^{2}(x)\tan(x))
limit as x approaches 0 of 5/(x-1)	\lim\:_{x\to\:0}(\frac{5}{x-1})
laplacetransform sin(2t+3)	laplacetransform\:\sin(2t+3)
area y=x,x>= 0	area\:y=x,x\ge\:0
integral of 1/(xsqrt(5x^2-3))	\int\:\frac{1}{x\sqrt{5x^{2}-3}}dx
maclaurin 6sin(2x)	maclaurin\:6\sin(2x)
integral of x^5sin(2x)	\int\:x^{5}\sin(2x)dx
derivative of 1/(1+ce^{-x})	\frac{d}{dx}(\frac{1}{1+ce^{-x}})
t(dy)/(dt)+30y= 1/t	t\frac{dy}{dt}+30y=\frac{1}{t}
integral of xe^{x/2}	\int\:xe^{\frac{x}{2}}dx
slope of (8.4)(5.2)	slope\:(8.4)(5.2)
integral of-(3000)/(x^2)	\int\:-\frac{3000}{x^{2}}dx
integral of (10x)/(sqrt(4x^2-4))	\int\:\frac{10x}{\sqrt{4x^{2}-4}}dx
inverse oflaplace ((s+3))/((s+7))	inverselaplace\:\frac{(s+3)}{(s+7)}
y^'+(2y)/t =(2cos(t^2))/t	y^{\prime\:}+\frac{2y}{t}=\frac{2\cos(t^{2})}{t}
integral of x*ln(x+1)	\int\:x\cdot\:\ln(x+1)dx
derivative of 3sin(3x)	derivative\:3\sin(3x)
integral of (x^4-6x^3+12x^2+6)/(x^3-6x^2+12x-8)	\int\:\frac{x^{4}-6x^{3}+12x^{2}+6}{x^{3}-6x^{2}+12x-8}dx
derivative of ((x+4(x^2-4x+16))/(x^3))	\frac{d}{dx}(\frac{(x+4)(x^{2}-4x+16)}{x^{3}})
derivative of 5sqrt(x)sin(x)	derivative\:5\sqrt{x}\sin(x)
integral of e^{-x}-1	\int\:e^{-x}-1dx
(\partial)/(\partial x)(-x^2)	\frac{\partial\:}{\partial\:x}(-x^{2})
(\partial ^2)/(\partial r\partial θ)(r(θ)*sin(θ))	\frac{\partial\:^{2}}{\partial\:r\partial\:θ}(r(θ)\cdot\:\sin(θ))
tangent of y=2x^4,(-2,32)	tangent\:y=2x^{4},(-2,32)
limit as x approaches 2 of-x	\lim\:_{x\to\:2}(-x)
derivative of (5x^2+25x/(5x))	\frac{d}{dx}(\frac{5x^{2}+25x}{5x})
integral of sqrt(10-x^2)	\int\:\sqrt{10-x^{2}}dx
integral of (xe^{-x^2})	\int\:(xe^{-x^{2}})dx
derivative of y=ln\|5+t-t^3\|	derivative\:y=\ln\left\|5+t-t^{3}\right\|
integral of (5cos(x)-4sin(x))	\int\:(5\cos(x)-4\sin(x))dx
maclaurin 1/(x-2)	maclaurin\:\frac{1}{x-2}
derivative of f(x)=e^{4x}	derivative\:f(x)=e^{4x}
(d^2)/(dx^2)(x^{8/9}+5x)	\frac{d^{2}}{dx^{2}}(x^{\frac{8}{9}}+5x)
integral from 3 to infinity of 1/x	\int\:_{3}^{\infty\:}\frac{1}{x}dx
integral from 0 to 4 of (x^2-4x)	\int\:_{0}^{4}(x^{2}-4x)dx
derivative of y=ln(-7x^6)	derivative\:y=\ln(-7x^{6})
(\partial)/(\partial x)(xsqrt(1+y^5))	\frac{\partial\:}{\partial\:x}(x\sqrt{1+y^{5}})
slope ofintercept (50,5119),(80,7219)	slopeintercept\:(50,5119),(80,7219)
integral of e^{2x}*cos(3x)	\int\:e^{2x}\cdot\:\cos(3x)dx
(\partial)/(\partial x)((1-x)^{1/2})	\frac{\partial\:}{\partial\:x}((1-x)^{\frac{1}{2}})

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