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Popular Calculus Problems

integral of ((ln(x)))/(x^3)	\int\:\frac{(\ln(x))}{x^{3}}dx
(dv)/(dt)=-kv	\frac{dv}{dt}=-kv
(dy}{dx}-(7y)/x =\frac{y^3)/(x^9)	\frac{dy}{dx}-\frac{7y}{x}=\frac{y^{3}}{x^{9}}
derivative of (3x^2/(2x+1))	\frac{d}{dx}(\frac{3x^{2}}{2x+1})
(dy)/(dx)=((x-2))/((y-2))	\frac{dy}{dx}=\frac{(x-2)}{(y-2)}
(1+cos(t))(dy)/(dt)=(1-e^{-y})sin(t)	(1+\cos(t))\frac{dy}{dt}=(1-e^{-y})\sin(t)
derivative of y=log_{5}(x)+log_{5}(x^4)	derivative\:y=\log_{5}(x)+\log_{5}(x^{4})
sum from n=1 to infinity}e^{-n of n^3	\sum\:_{n=1}^{\infty\:}e^{-n}n^{3}
(2xy^2-4)dx+(2x^2y+7)dy=0	(2xy^{2}-4)dx+(2x^{2}y+7)dy=0
slope of (7)(0.1)	slope\:(7)(0.1)
integral from pi/4 to pi/2 of cos(x)	\int\:_{\frac{π}{4}}^{\frac{π}{2}}\cos(x)dx
(\partial)/(\partial x)(-(9y)/(x^2+y^2+7))	\frac{\partial\:}{\partial\:x}(-\frac{9y}{x^{2}+y^{2}+7})
integral from 0 to 1 of x^{4/5}	\int\:_{0}^{1}x^{\frac{4}{5}}dx
integral of sqrt(100-x^2)	\int\:\sqrt{100-x^{2}}dx
integral of (x^4)/(sqrt(x^5+1))	\int\:\frac{x^{4}}{\sqrt{x^{5}+1}}dx
integral of 16	\int\:16dx
integral of (x^3)/(9-x^4)	\int\:\frac{x^{3}}{9-x^{4}}dx
integral of (1/(3+2x^2))	\int\:(\frac{1}{3+2x^{2}})dx
limit as t approaches 0+of (sin(t))/t	\lim\:_{t\to\:0+}(\frac{\sin(t)}{t})
derivative of x^3(4-x^2)	\frac{d}{dx}(x^{3}(4-x^{2}))
derivative of (x^2/2+1)	\frac{d}{dx}(\frac{x^{2}}{2}+1)
sum from n=0 to infinity of e/n	\sum\:_{n=0}^{\infty\:}\frac{e}{n}
(\partial)/(\partial x)(ln(t^2+1))	\frac{\partial\:}{\partial\:x}(\ln(t^{2}+1))
derivative of ax^5ln(x/2+bx^3(x-2))	\frac{d}{dx}(ax^{5}\ln(\frac{x}{2})+bx^{3}(x-2))
integral of (1+2x+x^2)/(3x+3x^2+x^3)	\int\:\frac{1+2x+x^{2}}{3x+3x^{2}+x^{3}}dx
f(x)=x^6ln(x)	f(x)=x^{6}\ln(x)
f(x)=-4sin(2x)	f(x)=-4\sin(2x)
t^2y^{''}-3ty^'-21y=0	t^{2}y^{\prime\:\prime\:}-3ty^{\prime\:}-21y=0
(\partial)/(\partial y)(x^2ye^{y/z})	\frac{\partial\:}{\partial\:y}(x^{2}ye^{\frac{y}{z}})
(\partial)/(\partial x)(3xsin(7x^2y))	\frac{\partial\:}{\partial\:x}(3x\sin(7x^{2}y))
(\partial)/(\partial x)(xe^y-ye^x)	\frac{\partial\:}{\partial\:x}(xe^{y}-ye^{x})
integral from 0 to 1 of (3^{3x}-1)/(3^x)	\int\:_{0}^{1}\frac{3^{3x}-1}{3^{x}}dx
derivative of y=(2x+1)+2/((2x+1)^3)	derivative\:y=(2x+1)+\frac{2}{(2x+1)^{3}}
integral from-1 to 1 of x(1-x)^2	\int\:_{-1}^{1}x(1-x)^{2}dx
limit as x approaches 0+of 1/(sin^2(x))	\lim\:_{x\to\:0+}(\frac{1}{\sin^{2}(x)})
derivative of (24x(x^2+1)/((1-x^2)^4))	\frac{d}{dx}(\frac{24x(x^{2}+1)}{(1-x^{2})^{4}})
integral of (x^2ln(x))/2	\int\:\frac{x^{2}\ln(x)}{2}dx
sum from n=0 to infinity of (n^2)/(e^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}}{e^{n}}
integral from 0 to pi of (cos(x))^6	\int\:_{0}^{π}(\cos(x))^{6}dx
integral from 2 to 4 of 2cos(pix)	\int\:_{2}^{4}2\cos(πx)dx
integral of sqrt(16-7x^2)	\int\:\sqrt{16-7x^{2}}dx
integral of (-1)/(1-2x+x^2)	\int\:\frac{-1}{1-2x+x^{2}}dx
limit as x approaches 0 of e^{csc(x)}	\lim\:_{x\to\:0}(e^{\csc(x)})
derivative of f(x)=(4x)/(9e^{5x)}	derivative\:f(x)=\frac{4x}{9e^{5x}}
slope ofintercept (5,-2),(-6,4)	slopeintercept\:(5,-2),(-6,4)
integral of sqrt(4x+3)	\int\:\sqrt{4x+3}dx
2xydy=(y^2+1)dx	2xydy=(y^{2}+1)dx
derivative of (3x/7)	\frac{d}{dx}(\frac{3x}{7})
integral of e^{2x}(1-7e^{2x})^2	\int\:e^{2x}(1-7e^{2x})^{2}dx
integral of (175)/(e^{-x)+1}	\int\:\frac{175}{e^{-x}+1}dx
derivative of ln(7x^2)	\frac{d}{dx}(\ln(7)x^{2})
derivative of f(x)=(3x+1)(x^2-2)	derivative\:f(x)=(3x+1)(x^{2}-2)
integral of 4/(sqrt(x^2-4x+13))	\int\:\frac{4}{\sqrt{x^{2}-4x+13}}dx
integral from 0 to 5 of 1/(x-3)	\int\:_{0}^{5}\frac{1}{x-3}dx
limit as θ approaches 0 of θ/(sin^2(θ))	\lim\:_{θ\to\:0}(\frac{θ}{\sin^{2}(θ)})
limit as x approaches 2 of x^2-7x+12	\lim\:_{x\to\:2}(x^{2}-7x+12)
inverse oflaplace 1/((s^3+s^2+s))	inverselaplace\:\frac{1}{(s^{3}+s^{2}+s)}
limit as x approaches 0 of (9sin(1))/1	\lim\:_{x\to\:0}(\frac{9\sin(1)}{1})
(dy)/(dx)+2xy=9x	\frac{dy}{dx}+2xy=9x
limit as x approaches 1 of (3x-1)^{10}	\lim\:_{x\to\:1}((3x-1)^{10})
integral from 0 to 1 of (e^{-x^2})	\int\:_{0}^{1}(e^{-x^{2}})dx
integral of acos(wt)	\int\:a\cos(wt)dt
derivative of (x-3^3(x+4)(x^2+1))	\frac{d}{dx}((x-3)^{3}(x+4)(x^{2}+1))
tangent of y=x-x^3	tangent\:y=x-x^{3}
integral of (cos(x))^5	\int\:(\cos(x))^{5}dx
(\partial)/(\partial y)((x-y)/(x+z))	\frac{\partial\:}{\partial\:y}(\frac{x-y}{x+z})
(dy)/(dx)=7xsqrt(y)	\frac{dy}{dx}=7x\sqrt{y}
limit as x approaches 0 of 3x+4	\lim\:_{x\to\:0}(3x+4)
integral of (cos^3(x)+4)/(cos^2(x))	\int\:\frac{\cos^{3}(x)+4}{\cos^{2}(x)}dx
integral of 3sin^2(x)cos^2(x)	\int\:3\sin^{2}(x)\cos^{2}(x)dx
(\partial)/(\partial y)((-x-7y)/(y^2+2x^2))	\frac{\partial\:}{\partial\:y}(\frac{-x-7y}{y^{2}+2x^{2}})
integral of 1/(sqrt(x)(1+\sqrt{x))^2}	\int\:\frac{1}{\sqrt{x}(1+\sqrt{x})^{2}}dx
limit as x approaches 4 of (-x+4)/x	\lim\:_{x\to\:4}(\frac{-x+4}{x})
derivative of e^{2x}(x-4(x+6))	\frac{d}{dx}(e^{2x}(x-4)(x+6))
integral of sin^8(x)*cos^5(x)	\int\:\sin^{8}(x)\cdot\:\cos^{5}(x)dx
derivative of (2x+8^2)	\frac{d}{dx}((2x+8)^{2})
integral of 2sqrt(x^3)	\int\:2\sqrt{x^{3}}dx
(2/t)^'	(\frac{2}{t})^{\prime\:}
maclaurin 1/(5x+7)	maclaurin\:\frac{1}{5x+7}
y^'=2y-y^3	y^{\prime\:}=2y-y^{3}
integral of 1/(x^2-3)	\int\:\frac{1}{x^{2}-3}dx
y^'=x+3y	y^{\prime\:}=x+3y
derivative of (1-2x)^{1/2}	derivative\:(1-2x)^{\frac{1}{2}}
integral of 1/((x+1)sqrt(x^2+2x-3))	\int\:\frac{1}{(x+1)\sqrt{x^{2}+2x-3}}dx
integral of ((1+cos(2x))/2)^2	\int\:(\frac{1+\cos(2x)}{2})^{2}dx
derivative of cos(ln(t))	derivative\:\cos(\ln(t))
x(dy)/(dx)+4y=x^{-3}e^x	x\frac{dy}{dx}+4y=x^{-3}e^{x}
integral of x/2	\int\:\frac{x}{2}dx
(\partial)/(\partial x)(2x^3y+3xy^2)	\frac{\partial\:}{\partial\:x}(2x^{3}y+3xy^{2})
integral of 2y^{3/2}	\int\:2y^{\frac{3}{2}}dy
integral of tan(8x+1)	\int\:\tan(8x+1)dx
integral of (3arctan(x))/(x^2)	\int\:\frac{3\arctan(x)}{x^{2}}dx
(\partial)/(\partial x)((e^x-2x)cos(y))	\frac{\partial\:}{\partial\:x}((e^{x}-2x)\cos(y))
(dy)/(dx)+ay-b=0	\frac{dy}{dx}+ay-b=0
tangent of f(x)=5x^2-4x-2,\at x=1	tangent\:f(x)=5x^{2}-4x-2,\at\:x=1
ty^'+10y= 1/t	ty^{\prime\:}+10y=\frac{1}{t}
integral of 7(cos(x)+sin(2x))/(sin(x))	\int\:7\frac{\cos(x)+\sin(2x)}{\sin(x)}dx
derivative of 1-e^{-2x}	derivative\:1-e^{-2x}
integral of 1/(10x-7)	\int\:\frac{1}{10x-7}dx
limit as x approaches 8 of e(3/((x-8)))	\lim\:_{x\to\:8}(e(\frac{3}{(x-8)}))

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