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Popular Calculus Problems

integral of (cos(x))/(sqrt(2sin(x)+1))	\int\:\frac{\cos(x)}{\sqrt{2\sin(x)+1}}dx
integral of sqrt(x*(4-x))	\int\:\sqrt{x\cdot\:(4-x)}dx
laplacetransform 5+4\delta(t)	laplacetransform\:5+4\delta(t)
integral of 4^{sin(x)}cos(x)	\int\:4^{\sin(x)}\cos(x)dx
limit as x approaches-7 of (x+8)/(x+7)	\lim\:_{x\to\:-7}(\frac{x+8}{x+7})
derivative of e^{x-3}	\frac{d}{dx}(e^{x-3})
derivative of 2x^5	derivative\:2x^{5}
integral of e^{-5x}sin(x)	\int\:e^{-5x}\sin(x)dx
derivative of (-cx/(x^2+y^2))	\frac{d}{dx}(\frac{-cx}{x^{2}+y^{2}})
sum from n=0 to infinity of 1/(4+e^{-n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{4+e^{-n}}
tangent of y=x^3-3x+1,(4,53)	tangent\:y=x^{3}-3x+1,(4,53)
tangent of y= x/(x+1)	tangent\:y=\frac{x}{x+1}
y^{'''}+5y^{''}=0	y^{\prime\:\prime\:\prime\:}+5y^{\prime\:\prime\:}=0
integral from 0 to 1 of (sqrt(x)-x^2)	\int\:_{0}^{1}(\sqrt{x}-x^{2})dx
derivative of-1/(sqrt(2^x))	\frac{d}{dx}(-\frac{1}{\sqrt{2^{x}}})
(\partial)/(\partial x)(10^{sqrt(x)})	\frac{\partial\:}{\partial\:x}(10^{\sqrt{x}})
derivative of (x^2-2x+3)/(x+1)	derivative\:\frac{x^{2}-2x+3}{x+1}
integral of 1/7	\int\:\frac{1}{7}dx
integral of sin(2x)ln(sin(2x))	\int\:\sin(2x)\ln(\sin(2x))dx
inverse oflaplace (10)/(s(s^2+2s+10))	inverselaplace\:\frac{10}{s(s^{2}+2s+10)}
(\partial)/(\partial y)(xy+y^2+y)	\frac{\partial\:}{\partial\:y}(xy+y^{2}+y)
tangent of f(x)= 2/(sqrt(x)),\at (1/9)	tangent\:f(x)=\frac{2}{\sqrt{x}},\at\:(\frac{1}{9})
integral of xarctan(4x)	\int\:x\arctan(4x)dx
tangent of x^2-4x+1	tangent\:x^{2}-4x+1
integral of sin(x)cos^6(x)	\int\:\sin(x)\cos^{6}(x)dx
limit as x approaches 0 of cos^2(x)	\lim\:_{x\to\:0}(\cos^{2}(x))
longdivision (x^2+1)/(x-2)	longdivision\:\frac{x^{2}+1}{x-2}
derivative of (x^4-2^5)	\frac{d}{dx}((x^{4}-2)^{5})
derivative of 8x^{3/2}	derivative\:8x^{\frac{3}{2}}
limit as x approaches-2 of 2x+1	\lim\:_{x\to\:-2}(2x+1)
slope of (1,-1),(6,-1 1/2)	slope\:(1,-1),(6,-1\frac{1}{2})
(\partial)/(\partial x)(e^{-t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-t}\cos(πx))
integral of tan(2x)sec^2(2x)	\int\:\tan(2x)\sec^{2}(2x)dx
integral of (e^t)/(e^{2t)+3e^t+2}	\int\:\frac{e^{t}}{e^{2t}+3e^{t}+2}dt
integral from sqrt(y) to 2 of 3/16 xy	\int\:_{\sqrt{y}}^{2}\frac{3}{16}xydx
tangent of sqrt(x^2+21),\at x=2	tangent\:\sqrt{x^{2}+21},\at\:x=2
limit as x approaches 1 of (4x-4)/(x-1)	\lim\:_{x\to\:1}(\frac{4x-4}{x-1})
integral of 16xsin(x)	\int\:16x\sin(x)dx
taylor (1+x)/(1-x)	taylor\:\frac{1+x}{1-x}
integral from 0 to e of ln(x)	\int\:_{0}^{e}\ln(x)dx
integral of (1+e)^x	\int\:(1+e)^{x}dx
(dy)/(dx)=(y^3)/(x^2)	\frac{dy}{dx}=\frac{y^{3}}{x^{2}}
integral of x^3(1-x^4)^5	\int\:x^{3}(1-x^{4})^{5}dx
integral of (7/(sqrt(1-x^2)))	\int\:(\frac{7}{\sqrt{1-x^{2}}})dx
integral of (1/(1+x^2))^2	\int\:(\frac{1}{1+x^{2}})^{2}dx
integral of 1/((a^2+x^2))	\int\:\frac{1}{(a^{2}+x^{2})}dx
y^'=((1-x-y))/(x+y)	y^{\prime\:}=\frac{(1-x-y)}{x+y}
1/4 q^{''}+20q^'+300q=0	\frac{1}{4}q^{\prime\:\prime\:}+20q^{\prime\:}+300q=0
integral of 2^X	\int\:2^{X}dX
derivative of 2/(x+1)	derivative\:\frac{2}{x+1}
(\partial)/(\partial x)((x+2y^3)^{1/3})	\frac{\partial\:}{\partial\:x}((x+2y^{3})^{\frac{1}{3}})
derivative of ((xcos(x+pi))/(x-pi))	\frac{d}{dx}(\frac{(x\cos(x)+π)}{x-π})
derivative of x^{-0.5}	derivative\:x^{-0.5}
(d^2)/(dx^2)(e^x)	\frac{d^{2}}{dx^{2}}(e^{x})
limit as x approaches 2 of sqrt(4x^2-2x)	\lim\:_{x\to\:2}(\sqrt{4x^{2}-2x})
integral of x*2^{-x}	\int\:x\cdot\:2^{-x}dx
(\partial)/(\partial x)(5e^{7x}sin(7y))	\frac{\partial\:}{\partial\:x}(5e^{7x}\sin(7y))
integral of (x^6-1/(x^6))^2	\int\:(x^{6}-\frac{1}{x^{6}})^{2}dx
integral of e^{x/9}	\int\:e^{\frac{x}{9}}dx
limit as θ approaches 0 of (cos(θ)-1)/(sin(θ))	\lim\:_{θ\to\:0}(\frac{\cos(θ)-1}{\sin(θ)})
area y=x^3+x^2,y=6x	area\:y=x^{3}+x^{2},y=6x
laplacetransform f(t)=2t^4	laplacetransform\:f(t)=2t^{4}
derivative of (e^x/(5x^2+1))	\frac{d}{dx}(\frac{e^{x}}{5x^{2}+1})
integral of pisin((nx)/2)	\int\:π\sin(\frac{nx}{2})dx
derivative of 6x^3-9x+4	\frac{d}{dx}(6x^{3}-9x+4)
limit as x approaches-1 of 4	\lim\:_{x\to\:-1}(4)
(\partial)/(\partial x)(f(y,x)(y/x))	\frac{\partial\:}{\partial\:x}(f(y,x)(\frac{y}{x}))
sum from n=1 to infinity}((-1)^{6n of)/n	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{6n}}{n}
(\partial)/(\partial x)(30y^2sqrt(x))	\frac{\partial\:}{\partial\:x}(30y^{2}\sqrt{x})
integral of-3x^2cos(x^3)	\int\:-3x^{2}\cos(x^{3})dx
integral from 8 to 16 of sqrt(256-x^2)	\int\:_{8}^{16}\sqrt{256-x^{2}}dx
integral from-pi to pi of sin(2x)	\int\:_{-π}^{π}\sin(2x)dx
derivative of (3x^2+x/(-x^2+3x-3))	\frac{d}{dx}(\frac{3x^{2}+x}{-x^{2}+3x-3})
(\partial)/(\partial x)((2xy)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{2xy}{x-y})
derivative of f(x)= x/7	derivative\:f(x)=\frac{x}{7}
area y=-x^2-8x-12,y=0,[-4,-1]	area\:y=-x^{2}-8x-12,y=0,[-4,-1]
derivative of f(x)=e^{-8x}	derivative\:f(x)=e^{-8x}
integral from 0 to 3 of x^2-6	\int\:_{0}^{3}x^{2}-6dx
integral from 0 to pi of 13sin^2(4x)	\int\:_{0}^{π}13\sin^{2}(4x)dx
inverse oflaplace ((s+1))/((s^2+s-1))	inverselaplace\:\frac{(s+1)}{(s^{2}+s-1)}
((dy)/(dx))+1/y = y/2+x/y	(\frac{dy}{dx})+\frac{1}{y}=\frac{y}{2}+\frac{x}{y}
derivative of f(x)=cy^{-5}	derivative\:f(x)=cy^{-5}
(\partial)/(\partial x)(ln(kt-mx))	\frac{\partial\:}{\partial\:x}(\ln(kt-mx))
(\partial)/(\partial x)(x/(y^2)-y/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{2}}-\frac{y}{x^{2}})
derivative of (x^2)^{-1}	derivative\:(x^{2})^{-1}
derivative of 1/((x^2-1(x^2+x+1)))	\frac{d}{dx}(\frac{1}{(x^{2}-1)(x^{2}+x+1)})
integral of 1/(x(10-x))	\int\:\frac{1}{x(10-x)}dx
(\partial)/(\partial x)((x+2)/(y+1))	\frac{\partial\:}{\partial\:x}(\frac{x+2}{y+1})
derivative of xe^{9x}	\frac{d}{dx}(xe^{9x})
derivative of 3/4 x^{4/3}-3/8 x^{2/3}+9	\frac{d}{dx}(\frac{3}{4}x^{\frac{4}{3}}-\frac{3}{8}x^{\frac{2}{3}}+9)
integral of ((a^x-b^x)^2)/(a^xb^x)	\int\:\frac{(a^{x}-b^{x})^{2}}{a^{x}b^{x}}dx
(dy)/(dx)=e^{7x-7y}	\frac{dy}{dx}=e^{7x-7y}
(\partial)/(\partial z)(2z)	\frac{\partial\:}{\partial\:z}(2z)
y^'+y=1	y^{\prime\:}+y=1
y^{''}+4y^'+4y=4-t	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=4-t
integral of x/(x^3)	\int\:\frac{x}{x^{3}}dx
integral of (x^3+e^x)	\int\:(x^{3}+e^{x})dx
sum from n=1 to infinity of n^{0.5}	\sum\:_{n=1}^{\infty\:}n^{0.5}
tangent of (2x)/(x+1)	tangent\:\frac{2x}{x+1}
integral from-1 to 1 of x^2(1-x^2)	\int\:_{-1}^{1}x^{2}(1-x^{2})dx

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