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Popular Calculus Problems

integral from 0 to 1 of (x/(x^2+1))	\int\:_{0}^{1}(\frac{x}{x^{2}+1})dx
integral from 3 to 7 of x/(x^2+6x+13)	\int\:_{3}^{7}\frac{x}{x^{2}+6x+13}dx
(1+x^2)(dy)/(dx)-2xy=x^2+x^4	(1+x^{2})\frac{dy}{dx}-2xy=x^{2}+x^{4}
(\partial)/(\partial x)(20e^{5x}y)	\frac{\partial\:}{\partial\:x}(20e^{5x}y)
f(x)=ln(x^2-1)	f(x)=\ln(x^{2}-1)
derivative of (x^2-6x/((x-3)^2))	\frac{d}{dx}(\frac{x^{2}-6x}{(x-3)^{2}})
integral of 3/((x-2)^2)	\int\:\frac{3}{(x-2)^{2}}dx
slope ofintercept (12,-16),(-9,8)	slopeintercept\:(12,-16),(-9,8)
derivative of (cos(x)/(1+cot(x)))	\frac{d}{dx}(\frac{\cos(x)}{1+\cot(x)})
integral from 0 to pi/4 of sin(3x)	\int\:_{0}^{\frac{π}{4}}\sin(3x)dx
derivative of (2(-x^2-4)/((x^2-4)^2))	\frac{d}{dx}(\frac{2(-x^{2}-4)}{(x^{2}-4)^{2}})
limit as x approaches 0 of (tan(4x))/(3x)	\lim\:_{x\to\:0}(\frac{\tan(4x)}{3x})
integral of 1/(cos(x))	\int\:\frac{1}{\cos(x)}dx
integral of (3x-11)/(x^3-5x^2)	\int\:\frac{3x-11}{x^{3}-5x^{2}}dx
integral of-8y^3	\int\:-8y^{3}dy
integral of e^{2x}cos(e^x)	\int\:e^{2x}\cos(e^{x})dx
y^{''}+9y=27	y^{\prime\:\prime\:}+9y=27
derivative of 8/(cos(x^2-2x))	\frac{d}{dx}(\frac{8}{\cos(x^{2}-2x)})
integral from 5 to 7 of x/(x^2+6x+13)	\int\:_{5}^{7}\frac{x}{x^{2}+6x+13}dx
(2x^{3/2})^'	(2x^{\frac{3}{2}})^{\prime\:}
t^2(dy)/(dt)-t=1+y+ty,y(1)=7	t^{2}\frac{dy}{dt}-t=1+y+ty,y(1)=7
integral from 0.2 to 0.4 of 300x	\int\:_{0.2}^{0.4}300xdx
(dy)/(dt)= y/(t+1)+4t^2+4t,y(1)=6	\frac{dy}{dt}=\frac{y}{t+1}+4t^{2}+4t,y(1)=6
integral of ((sin^3(x)))/(cos(x))	\int\:\frac{(\sin^{3}(x))}{\cos(x)}dx
integral of 1/(-csc(y))	\int\:\frac{1}{-\csc(y)}dy
derivative of e^{3x}cos(3x)	\frac{d}{dx}(e^{3x}\cos(3x))
integral of 19sin^2(xco)s^2x	\int\:19\sin^{2}(xco)s^{2}xdx
integral from-pi to pi of sin(3x)sin(3x)	\int\:_{-π}^{π}\sin(3x)\sin(3x)dx
derivative of y= 1/3 x^{3/2}	derivative\:y=\frac{1}{3}x^{\frac{3}{2}}
(\partial)/(\partial x)(2x^2+2y^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+2y^{2})
derivative of x/(sqrt(9-4x))	\frac{d}{dx}(\frac{x}{\sqrt{9-4x}})
y^{''}+9y=-24sin(3t)	y^{\prime\:\prime\:}+9y=-24\sin(3t)
(\partial)/(\partial r)(rcos(s))	\frac{\partial\:}{\partial\:r}(r\cos(s))
derivative of y=sqrt(5-x)	derivative\:y=\sqrt{5-x}
integral of 1/((144+x^2)^{3/2)}	\int\:\frac{1}{(144+x^{2})^{\frac{3}{2}}}dx
(dy)/(dx)=y(xy^7-1)	\frac{dy}{dx}=y(xy^{7}-1)
(dy)/(dt)+y=cos(t),y(0)=1	\frac{dy}{dt}+y=\cos(t),y(0)=1
derivative of 1/2 sqrt(x)	derivative\:\frac{1}{2}\sqrt{x}
integral from-1 to 3 of (x^2-4x+3)	\int\:_{-1}^{3}(x^{2}-4x+3)dx
integral of sin^2(2x)cos^2(2x)	\int\:\sin^{2}(2x)\cos^{2}(2x)dx
integral from 0 to pi/(12) of (sin(6x))/(1+cos^2(6x))	\int\:_{0}^{\frac{π}{12}}\frac{\sin(6x)}{1+\cos^{2}(6x)}dx
3y^{''}-2y^'+4y=0	3y^{\prime\:\prime\:}-2y^{\prime\:}+4y=0
derivative of 2sin(x^2-1)	\frac{d}{dx}(2\sin(x^{2}-1))
integral of 1/(sqrt(-x^2+4x+12))	\int\:\frac{1}{\sqrt{-x^{2}+4x+12}}dx
sum from n=1 to infinity of 8/(n^5)	\sum\:_{n=1}^{\infty\:}\frac{8}{n^{5}}
tangent of e^{-2x}	tangent\:e^{-2x}
(dy)/(dx)+y=5sin(2x)	\frac{dy}{dx}+y=5\sin(2x)
integral of (x+3)/(x-2)	\int\:\frac{x+3}{x-2}dx
derivative of (t^2)/(t-2)	derivative\:\frac{t^{2}}{t-2}
integral of (6x^5+7x)	\int\:(6x^{5}+7x)dx
(dy)/(dx)=(y^2)/(e^x),y(0)=-2	\frac{dy}{dx}=\frac{y^{2}}{e^{x}},y(0)=-2
limit as x approaches infinity of (sqrt(x))/(ln(x))	\lim\:_{x\to\:\infty\:}(\frac{\sqrt{x}}{\ln(x)})
derivative of (x/2+1^3)	\frac{d}{dx}((\frac{x}{2}+1)^{3})
integral of e^{6x}sin(x)	\int\:e^{6x}\sin(x)dx
derivative of f(x)=1.5x^7-(x^4)/3+pix-ex^2+sqrt(2)	derivative\:f(x)=1.5x^{7}-\frac{x^{4}}{3}+πx-ex^{2}+\sqrt{2}
integral from 0 to pi/4 of sin(x)	\int\:_{0}^{\frac{π}{4}}\sin(x)dx
derivative of (48)/((1-x)^4)	derivative\:\frac{48}{(1-x)^{4}}
integral of e^{2t}cos(5t)	\int\:e^{2t}\cos(5t)dt
(x^2+1)(dy)/(dx)=2xy	(x^{2}+1)\frac{dy}{dx}=2xy
limit as x approaches 0+of x^2ln(x)	\lim\:_{x\to\:0+}(x^{2}\ln(x))
limit as x approaches (1) of (x^8-1)/(x^5-1)	\lim\:_{x\to\:(1)}(\frac{x^{8}-1}{x^{5}-1})
integral of (6(1+s))/(s(s^2+7s+6))	\int\:\frac{6(1+s)}{s(s^{2}+7s+6)}ds
integral of sqrt(1-z^2)	\int\:\sqrt{1-z^{2}}
limit as h approaches 0 of 1/(sqrt(h))	\lim\:_{h\to\:0}(\frac{1}{\sqrt{h}})
limit as x approaches 0 of x/(sin(5x))	\lim\:_{x\to\:0}(\frac{x}{\sin(5x)})
integral from 0 to 4 of 1/(x^2-x-2)	\int\:_{0}^{4}\frac{1}{x^{2}-x-2}dx
integral from 0 to pi of x^2cos(nx)	\int\:_{0}^{π}x^{2}\cos(nx)dx
derivative of \|x^3+3x^2-24x-80\|	\frac{d}{dx}(\left\|x^{3}+3x^{2}-24x-80\right\|)
derivative of (3sin(x)/(3+cos(x)))	\frac{d}{dx}(\frac{3\sin(x)}{3+\cos(x)})
implicit (dy)/(dx),e^{xy}+x^2-y^2=12	implicit\:\frac{dy}{dx},e^{xy}+x^{2}-y^{2}=12
sum from n=0 to infinity of (1/17)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{17})^{n}
limit as x approaches 0 of (sin(5x))/(6x)	\lim\:_{x\to\:0}(\frac{\sin(5x)}{6x})
derivative of f(x)=3sec(5x)	derivative\:f(x)=3\sec(5x)
derivative of (1-6t)/(5+t)	derivative\:\frac{1-6t}{5+t}
integral of 11tan^4(xse)c^6x	\int\:11\tan^{4}(xse)c^{6}xdx
derivative of 1-e^{3x}	\frac{d}{dx}(1-e^{3x})
integral from 1 to 2 of (sqrt(x^2-1))/x	\int\:_{1}^{2}\frac{\sqrt{x^{2}-1}}{x}dx
laplacetransform tcos(2t)	laplacetransform\:t\cos(2t)
sum from k=0 to infinity of (e/(10))^k	\sum\:_{k=0}^{\infty\:}(\frac{e}{10})^{k}
limit as x approaches 1-of-x^2+3x-4	\lim\:_{x\to\:1-}(-x^{2}+3x-4)
derivative of e^x(cos(x))	\frac{d}{dx}(e^{x}(\cos(x)))
d/(dt)(t^2sin(wt))	\frac{d}{dt}(t^{2}\sin(wt))
taylor e^{5x}	taylor\:e^{5x}
taylor 1/((1-3x^2)),x=0.577	taylor\:\frac{1}{(1-3x^{2})},x=0.577
derivative of (2x^3+2)(x^4-3x)	derivative\:(2x^{3}+2)(x^{4}-3x)
integral of (u+1)/(u^2+1)	\int\:\frac{u+1}{u^{2}+1}du
derivative of f(x)=(e^x)/(1+e^x)	derivative\:f(x)=\frac{e^{x}}{1+e^{x}}
derivative of tan(x-0.5x)	\frac{d}{dx}(\tan(x)-0.5x)
(dy)/(dx)=xy-3x-2y+6	\frac{dy}{dx}=xy-3x-2y+6
integral of 5xln(x)	\int\:5x\ln(x)dx
tangent of f(x)=-1/x ,\at x=3	tangent\:f(x)=-\frac{1}{x},\at\:x=3
limit as x approaches-4 of-x^2+6x-8	\lim\:_{x\to\:-4}(-x^{2}+6x-8)
derivative of x/(sqrt(x-8))	\frac{d}{dx}(\frac{x}{\sqrt{x-8}})
d/(dt)(4cos(2t))	\frac{d}{dt}(4\cos(2t))
y^'= x/y+y/x	y^{\prime\:}=\frac{x}{y}+\frac{y}{x}
integral of 3sec^2(3x)	\int\:3\sec^{2}(3x)dx
derivative of (x^2^3)	\frac{d}{dx}((x^{2})^{3})
derivative of (sec(x)/(1+tan(x)))	\frac{d}{dx}(\frac{\sec(x)}{1+\tan(x)})
derivative of-0.0006x(x-15^2(x-40))	\frac{d}{dx}(-0.0006x(x-15)^{2}(x-40))
derivative of y=x(7x+3)^{1/3}	derivative\:y=x(7x+3)^{\frac{1}{3}}

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