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Popular Calculus Problems

integral of sqrt(1-(x^2)/4)	\int\:\sqrt{1-\frac{x^{2}}{4}}dx
integral of (2^t+e^pi)	\int\:(2^{t}+e^{π})dt
y^'=e^{4x}(cos(x)+sin(x))	y^{\prime\:}=e^{4x}(\cos(x)+\sin(x))
(\partial)/(\partial z)((x^2-y^2)/(z^2))	\frac{\partial\:}{\partial\:z}(\frac{x^{2}-y^{2}}{z^{2}})
derivative of ((6-sec(x))/(tan(x)))	\frac{d}{dx}(\frac{(6-\sec(x))}{\tan(x)})
sum from n=1 to infinity of (3/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{3}{2})^{n}
integral of (6x+4)/(3x^2+4x+5)	\int\:\frac{6x+4}{3x^{2}+4x+5}dx
area x^3-1,x=-1,x=2	area\:x^{3}-1,x=-1,x=2
derivative of (sec^2(x)/2)	\frac{d}{dx}(\frac{\sec^{2}(x)}{2})
integral from-10 to 10 of 1/(100+x^2)	\int\:_{-10}^{10}\frac{1}{100+x^{2}}dx
integral of (x+sqrt(x))	\int\:(x+\sqrt{x})dx
derivative of 3(x^2+5x)^3	derivative\:3(x^{2}+5x)^{3}
derivative of 6x*sin(3x^2)	\frac{d}{dx}(6x\cdot\:\sin(3x^{2}))
derivative of ln((4-x/(4+x)))	\frac{d}{dx}(\ln(\frac{4-x}{4+x}))
integral from 0 to 3 of c(3-x)	\int\:_{0}^{3}c(3-x)dx
integral of (5x-3)/(x+1)	\int\:\frac{5x-3}{x+1}dx
derivative of f(x)= 4/(3x^2)	derivative\:f(x)=\frac{4}{3x^{2}}
integral of (x^2e^x)/((x+2)^2)	\int\:\frac{x^{2}e^{x}}{(x+2)^{2}}dx
integral of-(18)/(x^{19)}	\int\:-\frac{18}{x^{19}}dx
(dx)/(dt)-x/(t-1)=t^2+2	\frac{dx}{dt}-\frac{x}{t-1}=t^{2}+2
limit as x approaches 0 of ((1+x)^2-1)/x	\lim\:_{x\to\:0}(\frac{(1+x)^{2}-1}{x})
y^'=1+9x-5y	y^{\prime\:}=1+9x-5y
integral of (cos(x))/(sin^4(x))	\int\:\frac{\cos(x)}{\sin^{4}(x)}dx
implicit y^2=x^2(x+1)	implicit\:y^{2}=x^{2}(x+1)
derivative of (6x)/(x^2+1)	derivative\:\frac{6x}{x^{2}+1}
(\partial)/(\partial y)(ye^x+sin(y))	\frac{\partial\:}{\partial\:y}(ye^{x}+\sin(y))
derivative of-7sin(7x)	derivative\:-7\sin(7x)
sum from n=1 to infinity of n/((n+1))	\sum\:_{n=1}^{\infty\:}\frac{n}{(n+1)}
derivative of e^{-x^2}-2e^{-x^2}x^2	\frac{d}{dx}(e^{-x^{2}}-2e^{-x^{2}}x^{2})
x^2y^'=xy+y^2	x^{2}y^{\prime\:}=xy+y^{2}
integral of x(x+4)^7	\int\:x(x+4)^{7}dx
integral of (10sin(2x))/(1+cos^4(x))	\int\:\frac{10\sin(2x)}{1+\cos^{4}(x)}dx
(dy)/(dx)y=ln(2)(x+3)	\frac{dy}{dx}y=\ln(2)(x+3)
integral of (x+8)/(2x^3-18x)	\int\:\frac{x+8}{2x^{3}-18x}dx
integral of ln(4)	\int\:\ln(4)
y^{''}-6y^'+9y=0,y(0)=3,y^'(0)= 25/3	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=3,y^{\prime\:}(0)=\frac{25}{3}
derivative of (x^4/4 ln(x)-(x^4)/(16))	\frac{d}{dx}(\frac{x^{4}}{4}\ln(x)-\frac{x^{4}}{16})
limit as x approaches-infinity of x+x^3	\lim\:_{x\to\:-\infty\:}(x+x^{3})
slope ofintercept (1.2)(4.4)	slopeintercept\:(1.2)(4.4)
integral of (x^3)/(x^2-81)	\int\:\frac{x^{3}}{x^{2}-81}dx
derivative of y(θ)=(sin(θ))/5+c/θ	derivative\:y(θ)=\frac{\sin(θ)}{5}+\frac{c}{θ}
integral of ((x-1)/x)^2	\int\:(\frac{x-1}{x})^{2}dx
derivative of 3(cos(x)^2)	\frac{d}{dx}(3(\cos(x))^{2})
sum from n=1 to infinity of 1/(2^n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}+1}
derivative of 1/(e^{x^2})	\frac{d}{dx}(\frac{1}{e^{x^{2}}})
derivative of 2e^x-8^x	\frac{d}{dx}(2e^{x}-8^{x})
integral of 1/(sqrt(x^2-144))	\int\:\frac{1}{\sqrt{x^{2}-144}}dx
(\partial)/(\partial x)(2y^3-6y+x^2)	\frac{\partial\:}{\partial\:x}(2y^{3}-6y+x^{2})
integral from 0 to pi/2 of xsin(x)	\int\:_{0}^{\frac{π}{2}}x\sin(x)dx
limit as x approaches 1 of+f(x)	\lim\:_{x\to\:1}(+f(x))
integral from 0 to 1 of 4-y-2sqrt(y)-1	\int\:_{0}^{1}4-y-2\sqrt{y}-1dy
integral of (3x^2+2)(2x^3+4x+1)^{1/2}	\int\:(3x^{2}+2)(2x^{3}+4x+1)^{\frac{1}{2}}dx
x^2((dy)/(dx))-2xy=3y^4	x^{2}(\frac{dy}{dx})-2xy=3y^{4}
derivative of 3+sqrt(x)	\frac{d}{dx}(3+\sqrt{x})
(dy)/(dx)=0.6y	\frac{dy}{dx}=0.6y
integral of e^{x^3}*x^2	\int\:e^{x^{3}}\cdot\:x^{2}dx
derivative of arctan(sinh(x))	\frac{d}{dx}(\arctan(\sinh(x)))
derivative of (ax^2+bx+ce^{-x/4})	\frac{d}{dx}((ax^{2}+bx+c)e^{-\frac{x}{4}})
tangent of f(x)=(14)/((1+e^{-x)),\at (0,7)}	tangent\:f(x)=\frac{14}{(1+e^{-x}),\at\:(0,7)}
integral of 1/((sin(x))^4)	\int\:\frac{1}{(\sin(x))^{4}}dx
(\partial)/(\partial y)(2x^3y+1)	\frac{\partial\:}{\partial\:y}(2x^{3}y+1)
derivative of 4+4x^{3/2}	\frac{d}{dx}(4+4x^{\frac{3}{2}})
sum from n=1 to infinity of (3/4)^n	\sum\:_{n=1}^{\infty\:}(\frac{3}{4})^{n}
d/(dt)(sin(2t))	\frac{d}{dt}(\sin(2t))
integral of e^{4x}cos(5x)	\int\:e^{4x}\cos(5x)dx
area 1/(14x^2), x/4 ,0,\sqrt[3]{1/14}	area\:\frac{1}{14x^{2}},\frac{x}{4},0,\sqrt[3]{\frac{1}{14}}
limit as x approaches 2+of (-4-x)/(7x-2)	\lim\:_{x\to\:2+}(\frac{-4-x}{7x-2})
integral of 3x^2-2x+3	\int\:3x^{2}-2x+3dx
derivative of-1/3 x^3	\frac{d}{dx}(-\frac{1}{3}x^{3})
y^'-ky=a+be^{-kt},y(0)=0	y^{\prime\:}-ky=a+be^{-kt},y(0)=0
integral of (-7sec(x)tan(x)+8sec^2(x))	\int\:(-7\sec(x)\tan(x)+8\sec^{2}(x))dx
derivative of a^x	\frac{d}{dx}(a^{x})
derivative of f(x)=2ln(2x)	derivative\:f(x)=2\ln(2x)
(dy)/(dx)+x^{-1}y=x^{-1}cos(x)y^{-2}	\frac{dy}{dx}+x^{-1}y=x^{-1}\cos(x)y^{-2}
integral from 1 to infinity of (1/x)	\int\:_{1}^{\infty\:}(\frac{1}{x})dx
xy^'+3y=(2e^{-2x})/(x^2)	xy^{\prime\:}+3y=\frac{2e^{-2x}}{x^{2}}
integral of 11e^x	\int\:11e^{x}dx
integral of x^4e^{xz}-2zsin(z^2)	\int\:x^{4}e^{xz}-2z\sin(z^{2})dz
integral of sec^6(3x)tan(3x)	\int\:\sec^{6}(3x)\tan(3x)dx
integral of sqrt(x)sin^2(x^{3/2}-4)	\int\:\sqrt{x}\sin^{2}(x^{\frac{3}{2}}-4)dx
sum from n=0 to infinity of (-3/4)^n	\sum\:_{n=0}^{\infty\:}(-\frac{3}{4})^{n}
area y=3x+1,(0,3)	area\:y=3x+1,(0,3)
(xdy)/(dx)=3xe^x-y+6x^2	\frac{xdy}{dx}=3xe^{x}-y+6x^{2}
(\partial)/(\partial x)(5x^3+4xy^3)	\frac{\partial\:}{\partial\:x}(5x^{3}+4xy^{3})
integral of (sqrt(x^2+1))/x	\int\:\frac{\sqrt{x^{2}+1}}{x}dx
sum from n=1 to infinity}(x^{n-1 of)/(sqrt(x))	\sum\:_{n=1}^{\infty\:}\frac{x^{n-1}}{\sqrt{x}}
limit as x approaches 1 of-1x^{-1-1}sin(1/x)-x^{-1-2}cos(1/x)	\lim\:_{x\to\:1}(-1x^{-1-1}\sin(\frac{1}{x})-x^{-1-2}\cos(\frac{1}{x}))
laplacetransform 2t+3	laplacetransform\:2t+3
area y=sqrt(x),y=x^2	area\:y=\sqrt{x},y=x^{2}
integral of ((x^2))/(sqrt(2x-x^2))	\int\:\frac{(x^{2})}{\sqrt{2x-x^{2}}}dx
derivative of f(x)=4sqrt(x)+6/(xsqrt(x))	derivative\:f(x)=4\sqrt{x}+\frac{6}{x\sqrt{x}}
integral of (2z)/(z^2+1)	\int\:\frac{2z}{z^{2}+1}dz
(\partial)/(\partial s)(ln(rs^8t^8)+1)	\frac{\partial\:}{\partial\:s}(\ln(rs^{8}t^{8})+1)
derivative of cos(sin(e^x))	derivative\:\cos(\sin(e^{x}))
integral from 1 to 2 of (2sqrt(x-1))/x	\int\:_{1}^{2}\frac{2\sqrt{x-1}}{x}dx
t((dy)/(dt))+5y=4t,y(1)=2	t(\frac{dy}{dt})+5y=4t,y(1)=2
derivative of x^{-3/2}	derivative\:x^{-\frac{3}{2}}
limit as x approaches+5 of x^2-2x+1	\lim\:_{x\to\:+5}(x^{2}-2x+1)
integral of (2+e^x)/(2-e^x)	\int\:\frac{2+e^{x}}{2-e^{x}}dx
(\partial)/(\partial x)(ln(e^{xy}cos(x)))	\frac{\partial\:}{\partial\:x}(\ln(e^{xy}\cos(x)))

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