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Popular Calculus Problems

(dy)/(dx)+y=-e^x	\frac{dy}{dx}+y=-e^{x}
limit as x approaches pi/2 of ln(cos(x))	\lim\:_{x\to\:\frac{π}{2}}(\ln(\cos(x)))
integral of t^2*cos(t)	\int\:t^{2}\cdot\:\cos(t)dt
derivative of x^3(x-7^2)	\frac{d}{dx}(x^{3}(x-7)^{2})
area y=x^2-4x+3,y=3+4x-x^2	area\:y=x^{2}-4x+3,y=3+4x-x^{2}
limit as x approaches-infinity of e^x	\lim\:_{x\to\:-\infty\:}(e^{x})
derivative of cos((pix)/4)	derivative\:\cos(\frac{πx}{4})
derivative of ln((x-1^2))	\frac{d}{dx}(\ln((x-1)^{2}))
area x=3y,x=y^2-4	area\:x=3y,x=y^{2}-4
integral of x^2e^{-λx}	\int\:x^{2}e^{-λx}dx
integral from 0 to 1 of 3/(1+t^2)	\int\:_{0}^{1}\frac{3}{1+t^{2}}dt
d/(dθ)(3-sin(θ))	\frac{d}{dθ}(3-\sin(θ))
tangent of f(x)=x^2-4,\at x=0	tangent\:f(x)=x^{2}-4,\at\:x=0
derivative of (3x^4+1/(x^3))	\frac{d}{dx}(\frac{3x^{4}+1}{x^{3}})
derivative of 2-(x^2-2x+4/(x-2))	\frac{d}{dx}(2-\frac{x^{2}-2x+4}{x-2})
integral of (sqrt(ln(x)))/x	\int\:\frac{\sqrt{\ln(x)}}{x}dx
x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2	x^{2}\frac{d^{2}y}{dx^{2}}-5xy^{\prime\:}+8y=4x^{2}
integral from 0 to 1 of 2pi(x+1)(x^2)	\int\:_{0}^{1}2π(x+1)(x^{2})dx
tangent of y=(sqrt(3))^x,\at x=6	tangent\:y=(\sqrt{3})^{x},\at\:x=6
integral of 1/((x+5)^2(x-4))	\int\:\frac{1}{(x+5)^{2}(x-4)}dx
derivative of-3t	derivative\:-3t
derivative of 6sin(sin(x))	\frac{d}{dx}(6\sin(\sin(x)))
integral of sin^3(xco)s^5x	\int\:\sin^{3}(xco)s^{5}xdx
derivative of f(x)=tan(2x)*sin(2x)	derivative\:f(x)=\tan(2x)\cdot\:\sin(2x)
integral from-3 to 3 of (18-2x^2)	\int\:_{-3}^{3}(18-2x^{2})dx
integral of x^3e^{x^4}	\int\:x^{3}e^{x^{4}}dx
6y^{''}+12y^'-18y=0	6y^{\prime\:\prime\:}+12y^{\prime\:}-18y=0
(\partial)/(\partial x)((x-2)(x^2+4))	\frac{\partial\:}{\partial\:x}((x-2)(x^{2}+4))
xv'+v=-(4-v+v^2)/(1-v+4v^2)	xv\prime\:+v=-\frac{4-v+v^{2}}{1-v+4v^{2}}
integral of (sqrt(64+x^2))/x	\int\:\frac{\sqrt{64+x^{2}}}{x}dx
limit as h approaches 0 of ((3^h-1))/h	\lim\:_{h\to\:0}(\frac{(3^{h}-1)}{h})
y^'=8+t-y	y^{\prime\:}=8+t-y
derivative of 3^{sin(x)}	derivative\:3^{\sin(x)}
integral of 1/8 e^{8x}	\int\:\frac{1}{8}e^{8x}dx
derivative of 9(2xe^x+e^xx^2)	\frac{d}{dx}(9(2xe^{x}+e^{x}x^{2}))
integral from 1 to 4 of 5/x	\int\:_{1}^{4}\frac{5}{x}dx
integral of x^2(1/(x^3)+1/(sqrt(x)))	\int\:x^{2}(\frac{1}{x^{3}}+\frac{1}{\sqrt{x}})dx
(dy}{dx}-\frac{2y)/x =x^2sin(3x)	\frac{dy}{dx}-\frac{2y}{x}=x^{2}\sin(3x)
integral of (cos(4x))/(1+sin^2(4x))	\int\:\frac{\cos(4x)}{1+\sin^{2}(4x)}dx
integral from 0 to 10 of 1	\int\:_{0}^{10}1
derivative of-x/(sqrt(4-x^2))	\frac{d}{dx}(-\frac{x}{\sqrt{4-x^{2}}})
derivative of w(z)=3z^7-7z^3+21z^2	derivative\:w(z)=3z^{7}-7z^{3}+21z^{2}
integral of (1-2x)/(sqrt(1-4x^2))	\int\:\frac{1-2x}{\sqrt{1-4x^{2}}}dx
(\partial)/(\partial y)(e^{2y}-ycos(xy))	\frac{\partial\:}{\partial\:y}(e^{2y}-y\cos(xy))
integral of 7e^{-0.1x}	\int\:7e^{-0.1x}dx
integral of sqrt(sin^2(x))	\int\:\sqrt{\sin^{2}(x)}dx
derivative of 7x^2cos(xcot(x))	\frac{d}{dx}(7x^{2}\cos(x)\cot(x))
(d^2)/(dx^2)(x/y)	\frac{d^{2}}{dx^{2}}(\frac{x}{y})
integral of 3x^2ln(x^2+5)	\int\:3x^{2}\ln(x^{2}+5)dx
limit as x approaches 0 of x[ln(x)]^2	\lim\:_{x\to\:0}(x[\ln(x)]^{2})
integral of ((1+e^x))/(e^x)	\int\:\frac{(1+e^{x})}{e^{x}}dx
limit as x approaches 1 of (x-1)^{x-1}	\lim\:_{x\to\:1}((x-1)^{x-1})
integral of 1/θ	\int\:\frac{1}{θ}dθ
integral from 3.5 to 4.5 of x/8	\int\:_{3.5}^{4.5}\frac{x}{8}dx
integral of ((2x+1)^2)/(x+2)	\int\:\frac{(2x+1)^{2}}{x+2}dx
integral of 5sec(x)tan(x)	\int\:5\sec(x)\tan(x)dx
(\partial)/(\partial x)(-2x^2y-y)	\frac{\partial\:}{\partial\:x}(-2x^{2}y-y)
integral of-sin(x)+cos(x)	\int\:-\sin(x)+\cos(x)dx
integral of 1/(sqrt(x^2+625))	\int\:\frac{1}{\sqrt{x^{2}+625}}dx
limit as x approaches 0 of (\|x\|)/(x^3-5)	\lim\:_{x\to\:0}(\frac{\left\|x\right\|}{x^{3}-5})
tangent of y=8x^2-5x^{11}	tangent\:y=8x^{2}-5x^{11}
integral of (x-2)e^{x+3}	\int\:(x-2)e^{x+3}dx
(\partial)/(\partial x)(4x^2-y^2+2y)	\frac{\partial\:}{\partial\:x}(4x^{2}-y^{2}+2y)
area y= x/3 ,y=sqrt(x-2)	area\:y=\frac{x}{3},y=\sqrt{x-2}
derivative of sqrt(2x^2+4x+5)	\frac{d}{dx}(\sqrt{2x^{2}+4x+5})
e^{x+3y}dy=xdx	e^{x+3y}dy=xdx
integral of 8/(x^2+1)	\int\:\frac{8}{x^{2}+1}dx
integral of (x^2)/(sqrt(x^2+2x+2))	\int\:\frac{x^{2}}{\sqrt{x^{2}+2x+2}}dx
(\partial)/(\partial x)(x+2y-1)	\frac{\partial\:}{\partial\:x}(x+2y-1)
area-x^2-3x,[-6,-1]	area\:-x^{2}-3x,[-6,-1]
(\partial)/(\partial y)(2y)	\frac{\partial\:}{\partial\:y}(2y)
xy^'+4y=5x	xy^{\prime\:}+4y=5x
d/(dy)((x^2)/(x^2+y^2))	\frac{d}{dy}(\frac{x^{2}}{x^{2}+y^{2}})
limit as x approaches infinity of 2^x+1	\lim\:_{x\to\:\infty\:}(2^{x}+1)
limit as x approaches-2 of f(x)	\lim\:_{x\to\:-2}(f(x))
integral from-3 to 3 of x^2-9	\int\:_{-3}^{3}x^{2}-9dx
(xsec(y/x)+y)dx-xdy=0	(x\sec(\frac{y}{x})+y)dx-xdy=0
y=(2^x)/2+(12)/(sqrt(x))	y=\frac{2^{x}}{2}+\frac{12}{\sqrt{x}}
tangent of f(x)=5e^{4x}+e^{-x^2},\at x=1	tangent\:f(x)=5e^{4x}+e^{-x^{2}},\at\:x=1
derivative of f(x)=6x^2	derivative\:f(x)=6x^{2}
24y^{''}+13y^'-2y=0	24y^{\prime\:\prime\:}+13y^{\prime\:}-2y=0
slope of (6,-8),(-2,7)	slope\:(6,-8),(-2,7)
integral of-csc(5x)cot(5x)	\int\:-\csc(5x)\cot(5x)dx
limit as x approaches 4-of (2-x)/(x-4)	\lim\:_{x\to\:4-}(\frac{2-x}{x-4})
derivative of arcsin(sin(x))	derivative\:\arcsin(\sin(x))
derivative of 1/(xln(10))	\frac{d}{dx}(\frac{1}{x\ln(10)})
derivative of f(x)=(1+e^x)/(1-e^x)	derivative\:f(x)=\frac{1+e^{x}}{1-e^{x}}
(dy)/(dx)=e^{(3x+2y)}	\frac{dy}{dx}=e^{(3x+2y)}
tangent of f(x)=sqrt(x^2+3x),\at x=1	tangent\:f(x)=\sqrt{x^{2}+3x},\at\:x=1
derivative of 4-(15/(4x^{1/4)})	\frac{d}{dx}(4-\frac{15}{4x^{\frac{1}{4}}})
derivative of \|x^3+3x^2-8\|	\frac{d}{dx}(\left\|x^{3}+3x^{2}-8\right\|)
integral of 3cos^3(2x)	\int\:3\cos^{3}(2x)dx
maclaurin e^xcos(x)	maclaurin\:e^{x}\cos(x)
d/(dt)(2)	\frac{d}{dt}(2)
derivative of f(x)=(-9x^3+2x^2)^5	derivative\:f(x)=(-9x^{3}+2x^{2})^{5}
integral of e^x*2	\int\:e^{x}\cdot\:2dx
derivative of x/(x+1)	derivative\:\frac{x}{x+1}
derivative of (1/(y^2)-7/(y^4))(y-3y^3)	derivative\:(\frac{1}{y^{2}}-\frac{7}{y^{4}})(y-3y^{3})
(\partial)/(\partial y)(sin(x+2y+3z))	\frac{\partial\:}{\partial\:y}(\sin(x+2y+3z))
integral of 2cos^3(3x)	\int\:2\cos^{3}(3x)dx

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