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Popular Calculus Problems

integral of 5e^x-1/x	\int\:5e^{x}-\frac{1}{x}dx
derivative of sin(2arccos(x))	derivative\:\sin(2\arccos(x))
integral from 0 to pi/(18) of cos(6x)	\int\:_{0}^{\frac{π}{18}}\cos(6x)dx
integral from 0 to x of 0	\int\:_{0}^{x}0
limit as x approaches+0+of ln(9/(x^3))	\lim\:_{x\to\:+0+}(\ln(\frac{9}{x^{3}}))
integral of 25cos^2(x)	\int\:25\cos^{2}(x)dx
(\partial)/(\partial x)(ln(2x))	\frac{\partial\:}{\partial\:x}(\ln(2x))
y^'-9/x y=(y^4)/(x^{12)}	y^{\prime\:}-\frac{9}{x}y=\frac{y^{4}}{x^{12}}
(dy)/(dt)=-y^2t-y^2t^2	\frac{dy}{dt}=-y^{2}t-y^{2}t^{2}
(d^2y)/(dx^2)+2/x (dy)/(dx)=3x+4	\frac{d^{2}y}{dx^{2}}+\frac{2}{x}\frac{dy}{dx}=3x+4
limit as x approaches 2-of 2-1/(x-2)	\lim\:_{x\to\:2-}(2-\frac{1}{x-2})
(dy)/(dx)=(4x^2+2x)/(y^2)	\frac{dy}{dx}=\frac{4x^{2}+2x}{y^{2}}
tangent of f(x)= 1/(x^2),1,\at x=1	tangent\:f(x)=\frac{1}{x^{2}},1,\at\:x=1
limit as x approaches 7 of (x^7)/(700)	\lim\:_{x\to\:7}(\frac{x^{7}}{700})
sum from n=0 to infinity of 4(3/5)^n	\sum\:_{n=0}^{\infty\:}4(\frac{3}{5})^{n}
limit as x approaches 1 of (2^x-2)/(x-1)	\lim\:_{x\to\:1}(\frac{2^{x}-2}{x-1})
integral of tan^2(x)	\int\:\tan^{2}(x)dx
inverse oflaplace (e^{-2s})/(s^3)	inverselaplace\:\frac{e^{-2s}}{s^{3}}
integral of sqrt(x)*e^x	\int\:\sqrt{x}\cdot\:e^{x}dx
derivative of 2sin(t)cos(t)	derivative\:2\sin(t)\cos(t)
y^{''}-4y^'+5=0	y^{\prime\:\prime\:}-4y^{\prime\:}+5=0
tangent of f(x)= 5/(2sqrt(5x+6)),\at a=2	tangent\:f(x)=\frac{5}{2\sqrt{5x+6}},\at\:a=2
area y=(x^3)/9 ,0<= x<= 2	area\:y=\frac{x^{3}}{9},0\le\:x\le\:2
ty^'+7y=t^2-t+1,y(1)= 1/7	ty^{\prime\:}+7y=t^{2}-t+1,y(1)=\frac{1}{7}
integral of tan^2(x	\int\:\tan^{2}(d)xdx
derivative of ln(x)	\frac{d}{dx}(\ln(x))
limit as x approaches 2-of-1/(x^2-4)	\lim\:_{x\to\:2-}(-\frac{1}{x^{2}-4})
f(x)=3sqrt(x)-1/x	f(x)=3\sqrt{x}-\frac{1}{x}
derivative of 0.04e^xx^2	\frac{d}{dx}(0.04e^{x}x^{2})
limit as x approaches 3 of j(x)	\lim\:_{x\to\:3}(j(x))
y^'=(cos(9x))/(e^{9y)}	y^{\prime\:}=\frac{\cos(9x)}{e^{9y}}
d/(dy)(3x+x^2y)	\frac{d}{dy}(3x+x^{2}y)
tangent of f(x)=6sin(x),\at x= pi/6	tangent\:f(x)=6\sin(x),\at\:x=\frac{π}{6}
tangent of 20sqrt(x)	tangent\:20\sqrt{x}
integral of 4x^3e^{7x^4}	\int\:4x^{3}e^{7x^{4}}dx
integral of x^{-8/5}	\int\:x^{-\frac{8}{5}}dx
derivative of ((1-cos(x)/(1+cos(x)))^3)	\frac{d}{dx}((\frac{1-\cos(x)}{1+\cos(x)})^{3})
derivative of e^tsin(5t)	derivative\:e^{t}\sin(5t)
inverse oflaplace 4/(s^4+4)	inverselaplace\:\frac{4}{s^{4}+4}
limit as x approaches 0 of 0/(x^2)	\lim\:_{x\to\:0}(\frac{0}{x^{2}})
sum from n=1 to infinity of (n^3)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{n^{3}}{n!}
derivative of 6x+5xe^x	derivative\:6x+5xe^{x}
implicit (dy)/(dx),1+ln(3xy)=e^{3x-y}	implicit\:\frac{dy}{dx},1+\ln(3xy)=e^{3x-y}
(\partial)/(\partial x)(3y^2-6y)	\frac{\partial\:}{\partial\:x}(3y^{2}-6y)
integral of (x^2+3)^5x	\int\:(x^{2}+3)^{5}xdx
sum from n=1 to infinity}((-1)^{n+1 of)((cos(npi))/(n^2))	\sum\:_{n=1}^{\infty\:}((-1)^{n+1})(\frac{\cos(nπ)}{n^{2}})
laplacetransform 6e^{5t}cos(2t)	laplacetransform\:6e^{5t}\cos(2t)
f(x)=x^{5/2}e^x	f(x)=x^{\frac{5}{2}}e^{x}
derivative of 2x+5	derivative\:2x+5
6y^{''}+y^'-y=0,y(0)=-1,y^'(0)=3	6y^{\prime\:\prime\:}+y^{\prime\:}-y=0,y(0)=-1,y^{\prime\:}(0)=3
(\partial)/(\partial x)(e^{x^2})	\frac{\partial\:}{\partial\:x}(e^{x^{2}})
derivative of g(x)=(2x-sqrt(x))(5x+2)	derivative\:g(x)=(2x-\sqrt{x})(5x+2)
(dy)/(dt)=t^2(1+15y)	\frac{dy}{dt}=t^{2}(1+15y)
(\partial)/(\partial x)(x^2sin(3x-2y))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(3x-2y))
limit as x approaches a of g(x)	\lim\:_{x\to\:a}(g(x))
integral of 3x^2+15x-11	\int\:3x^{2}+15x-11dx
y^{''}+y=t	y^{\prime\:\prime\:}+y=t
integral of (sin^7(x))/(cos^4(x))	\int\:\frac{\sin^{7}(x)}{\cos^{4}(x)}dx
y^{''}-4y^'-5y=9e^2t	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=9e^{2}t
integral of rcos(r)	\int\:r\cos(r)dr
tangent of 2/(5x+3),\at x=-1	tangent\:\frac{2}{5x+3},\at\:x=-1
derivative of ((x+1(2x-3))/(2x+3))	\frac{d}{dx}(\frac{(x+1)(2x-3)}{2x+3})
integral of cos^3(x/9)	\int\:\cos^{3}(\frac{x}{9})dx
integral of sin^4(z)	\int\:\sin^{4}(z)
tangent of f(x)=4x-3x^2,(2,-4)	tangent\:f(x)=4x-3x^{2},(2,-4)
derivative of y= x/(1-5x)	derivative\:y=\frac{x}{1-5x}
(x^2+1)y^'+3x(y-1)=0	(x^{2}+1)y^{\prime\:}+3x(y-1)=0
derivative of (-25x^2+9^2)	\frac{d}{dx}((-25x^{2}+9)^{2})
derivative of 9cos(4x)	derivative\:9\cos(4x)
limit as x approaches-1 of 2/((x+1)^3)	\lim\:_{x\to\:-1}(\frac{2}{(x+1)^{3}})
integral of (sec^2(x)-8)	\int\:(\sec^{2}(x)-8)dx
integral of sqrt(cos(2x))sin(2x)	\int\:\sqrt{\cos(2x)}\sin(2x)dx
laplacetransform 1/2+1/2*cos(2t)	laplacetransform\:\frac{1}{2}+\frac{1}{2}\cdot\:\cos(2t)
integral of (2000)/(sqrt(300x))	\int\:\frac{2000}{\sqrt{300x}}dx
derivative of-3/2 sqrt(x^3)-2x^5-5x^2	\frac{d}{dx}(-\frac{3}{2}\sqrt{x^{3}}-2x^{5}-5x^{2})
derivative of 1+3sqrt(x)	\frac{d}{dx}(1+3\sqrt{x})
(dy)/(dx)= 1/(4y^3)	\frac{dy}{dx}=\frac{1}{4y^{3}}
derivative of (x^2-49/(x-7))	\frac{d}{dx}(\frac{x^{2}-49}{x-7})
integral of sqrt(2+2sin(θ))	\int\:\sqrt{2+2\sin(θ)}dθ
limit as x approaches 0 of 1/(x^2-1)	\lim\:_{x\to\:0}(\frac{1}{x^{2}-1})
y^'(x)=(3x^2)/(3y^2-11),y(1)=0	y^{\prime\:}(x)=\frac{3x^{2}}{3y^{2}-11},y(1)=0
derivative of x^2-3x+3	derivative\:x^{2}-3x+3
(dy)/(dx)=2x+3y-1	\frac{dy}{dx}=2x+3y-1
integral of (y^3)	\int\:(y^{3})dy
integral of (7(1-tan^2(x)))/(sec^2(x))	\int\:\frac{7(1-\tan^{2}(x))}{\sec^{2}(x)}dx
tangent of y=3x^2+4	tangent\:y=3x^{2}+4
integral of (x+2)	\int\:(x+2)dx
(\partial)/(\partial x)(5x^{7y})	\frac{\partial\:}{\partial\:x}(5x^{7y})
integral of 56xe^{7x^2}	\int\:56xe^{7x^{2}}dx
y^'+2y^2cos(x+1)=0	y^{\prime\:}+2y^{2}\cos(x+1)=0
derivative of {f}(x*{f}(x))	\frac{d}{dx}({f}(x)\cdot\:{f}(x))
limit as x approaches 4-of arcsin(x/4)	\lim\:_{x\to\:4-}(\arcsin(\frac{x}{4}))
limit as x approaches 0 of (x^2h+3xh^2+h^3)/(2xh+5h^2)	\lim\:_{x\to\:0}(\frac{x^{2}h+3xh^{2}+h^{3}}{2xh+5h^{2}})
area y=sqrt(x+2),y= 1/(x+1),x=2,x=0	area\:y=\sqrt{x+2},y=\frac{1}{x+1},x=2,x=0
(\partial)/(\partial x)(e^{yln(x)})	\frac{\partial\:}{\partial\:x}(e^{y\ln(x)})
derivative of 2bx	\frac{d}{dx}(2bx)
limit as x approaches infinity of 1/(xln(x)(ln(ln(x)))^{-1)}	\lim\:_{x\to\:\infty\:}(\frac{1}{x\ln(x)(\ln(\ln(x)))^{-1}})
integral of 5e^{6x}+(-3x^6+4x)/(x^2)	\int\:5e^{6x}+\frac{-3x^{6}+4x}{x^{2}}dx
area e^x,x^2-1,-1.1,2	area\:e^{x},x^{2}-1,-1.1,2
integral of 1/(x^2sqrt(x^2+3))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+3}}dx

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