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Popular Calculus Problems

integral of (2x^2)/3	\int\:\frac{2x^{2}}{3}dx
integral of sin(12x)\sqrt[3]{cos(12x)}	\int\:\sin(12x)\sqrt[3]{\cos(12x)}dx
integral of 5xe^{3x^2}	\int\:5xe^{3x^{2}}dx
integral of 7sin(x)cos(x)	\int\:7\sin(x)\cos(x)dx
d/(dt)((csc^2(t))/(-cot(t)(csc(t))))	\frac{d}{dt}(\frac{\csc^{2}(t)}{-\cot(t)(\csc(t))})
sum from n=1 to infinity of tan(1/n)	\sum\:_{n=1}^{\infty\:}\tan(\frac{1}{n})
y^'+3x^2y=10x^2	y^{\prime\:}+3x^{2}y=10x^{2}
((t^2+1)dy)/(dt)+ty=0,y(0)=3	\frac{(t^{2}+1)dy}{dt}+ty=0,y(0)=3
derivative of 3+sqrt(5x)	\frac{d}{dx}(3+\sqrt{5x})
(\partial)/(\partial x)(4x+cy+2z)	\frac{\partial\:}{\partial\:x}(4x+cy+2z)
integral of sin(x)(cot(x)+csc(x))	\int\:\sin(x)(\cot(x)+\csc(x))dx
integral of cos(5t)e^t	\int\:\cos(5t)e^{t}dt
integral of tan^2(θ)	\int\:\tan^{2}(θ)dθ
derivative of cos(pixpi)	\frac{d}{dx}(\cos(πx)π)
integral of 1/(e^{ax)}	\int\:\frac{1}{e^{ax}}dx
derivative of f(x)=5x-2	derivative\:f(x)=5x-2
derivative of f(x)=(5x^3+1)/(2x-3)	derivative\:f(x)=\frac{5x^{3}+1}{2x-3}
integral of (5t-3)/(t+1)	\int\:\frac{5t-3}{t+1}dt
sum from n=0 to infinity of 1/((2n+1)!)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n+1)!}
(\partial)/(\partial x)(2xe^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(2xe^{\sqrt{xy}})
limit as x approaches 6 of (3x)/(x^2-6x)	\lim\:_{x\to\:6}(\frac{3x}{x^{2}-6x})
integral from 1 to infinity of sqrt(x)	\int\:_{1}^{\infty\:}\sqrt{x}dx
(dy)/(dx)= y/x+3x+7	\frac{dy}{dx}=\frac{y}{x}+3x+7
factor 3x^4-12x^3	factor\:3x^{4}-12x^{3}
derivative of sin^5(x/3)	\frac{d}{dx}(\sin^{5}(\frac{x}{3}))
integral of x/((x+4)^2)	\int\:\frac{x}{(x+4)^{2}}dx
limit as t approaches 3 of 2t^{-1}	\lim\:_{t\to\:3}(2t^{-1})
integral of ((x^2-x+28))/(x^3+7x)	\int\:\frac{(x^{2}-x+28)}{x^{3}+7x}dx
y^'(t)=(y-1)(y+1),y(0)=3	y^{\prime\:}(t)=(y-1)(y+1),y(0)=3
integral of sin(1-3x)	\int\:\sin(1-3x)dx
integral of (5x^3-6x+4)/(x^3-x^2)	\int\:\frac{5x^{3}-6x+4}{x^{3}-x^{2}}dx
derivative of 2x^{3/2}+3	\frac{d}{dx}(2x^{\frac{3}{2}}+3)
derivative of (arctan(3x))^2	derivative\:(\arctan(3x))^{2}
derivative of 15sin(-pixtan(2/3 pix))	\frac{d}{dx}(15\sin(-πx)\tan(\frac{2}{3}πx))
integral of (2-v)/(v^2+2v-3)	\int\:\frac{2-v}{v^{2}+2v-3}dv
(\partial)/(\partial x)(x^3+axy^2)	\frac{\partial\:}{\partial\:x}(x^{3}+axy^{2})
limit as x approaches-infinity of (4arctan(8x))/(e^x+2)	\lim\:_{x\to\:-\infty\:}(\frac{4\arctan(8x)}{e^{x}+2})
y^'-2y=3e^{2x}	y^{\prime\:}-2y=3e^{2x}
derivative of sec^4(x)	derivative\:\sec^{4}(x)
integral of (3x)/((x^2+1))	\int\:\frac{3x}{(x^{2}+1)}dx
derivative of (4x^2-16/(x-2))	\frac{d}{dx}(\frac{4x^{2}-16}{x-2})
tangent of f(x)= 1/(sqrt(x)),(1,1)	tangent\:f(x)=\frac{1}{\sqrt{x}},(1,1)
derivative of arccos(e^{9x})	derivative\:\arccos(e^{9x})
derivative of 0.5sin(2x)	\frac{d}{dx}(0.5\sin(2x))
area x^2-4x+3,-x^2+2x+3	area\:x^{2}-4x+3,-x^{2}+2x+3
integral of (x^2-4)	\int\:(x^{2}-4)dx
area y= 1/(20x^2),x=y,y= x/(16)	area\:y=\frac{1}{20x^{2}},x=y,y=\frac{x}{16}
integral of x*y	\int\:x\cdot\:y
derivative of (x^2+1sqrt(x))	\frac{d}{dx}((x^{2}+1)\sqrt{x})
derivative of (3x^4-18x^5*cos(5x^2))	\frac{d}{dx}((3x^{4}-18x)^{5}\cdot\:\cos(5x^{2}))
(yx-y)dy-(y+1)dx=0	(yx-y)dy-(y+1)dx=0
integral of e^{-x}*sin(2x)	\int\:e^{-x}\cdot\:\sin(2x)dx
integral of (arctan(x)-ln(x))	\int\:(\arctan(x)-\ln(x))dx
integral of (12x+7)	\int\:(12x+7)dx
taylor (x^2+25)^{-3}	taylor\:(x^{2}+25)^{-3}
limit as x approaches-4-of (-6x)/(x+4)	\lim\:_{x\to\:-4-}(\frac{-6x}{x+4})
derivative of 3cos(5ln(x))	derivative\:3\cos(5\ln(x))
(\partial)/(\partial y)(4x)	\frac{\partial\:}{\partial\:y}(4x)
integral from 0 to ln(12) of xe^x	\int\:_{0}^{\ln(12)}xe^{x}dx
limit as x approaches infinity of (1+sin(6x))^{1/(3x)}	\lim\:_{x\to\:\infty\:}((1+\sin(6x))^{\frac{1}{3x}})
limit as t approaches infinity of (1-e^{-2t})/t	\lim\:_{t\to\:\infty\:}(\frac{1-e^{-2t}}{t})
integral of 1/(sqrt(x^2-2x+5))	\int\:\frac{1}{\sqrt{x^{2}-2x+5}}dx
derivative of arctan(e^{-x})	\frac{d}{dx}(\arctan(e^{-x}))
derivative of e^{3sqrt(x)}	derivative\:e^{3\sqrt{x}}
limit as n approaches infinity of (n^{sqrt(2)})/(21^n)	\lim\:_{n\to\:\infty\:}(\frac{n^{\sqrt{2}}}{21^{n}})
laplacetransform 5t^2-2e^t	laplacetransform\:5t^{2}-2e^{t}
derivative of-k/(x^2)	\frac{d}{dx}(-\frac{k}{x^{2}})
derivative of x^3-8x^2+19x-12	derivative\:x^{3}-8x^{2}+19x-12
integral from 5 to 10 of (3x+3)	\int\:_{5}^{10}(3x+3)dx
integral of 1/(t^3+t^2-2t)	\int\:\frac{1}{t^{3}+t^{2}-2t}dt
integral of (32x^2)/((x-15)(x+5)^2)	\int\:\frac{32x^{2}}{(x-15)(x+5)^{2}}dx
integral of 8^{-x}	\int\:8^{-x}dx
derivative of 1/(sec^2(4x))	\frac{d}{dx}(\frac{1}{\sec^{2}(4x)})
derivative of f(x)=ln(6)-3x^5	derivative\:f(x)=\ln(6)-3x^{5}
derivative of (x^2)/(x^2+1)	derivative\:\frac{x^{2}}{x^{2}+1}
limit as x approaches infinity of 52.2+(41.9e^{(-0.055x)})	\lim\:_{x\to\:\infty\:}(52.2+(41.9\cdot\:e^{(-0.055\cdot\:x)}))
derivative of ln(x^2+y)	\frac{d}{dx}(\ln(x^{2}+y))
limit as x approaches-infinity of 0x	\lim\:_{x\to\:-\infty\:}(0x)
integral of 2x+22	\int\:2x+22dx
f(x)=ln(x)cos(x)	f(x)=\ln(x)\cos(x)
inverse oflaplace 1/(9s)	inverselaplace\:\frac{1}{9s}
(dv)/(dt)=(457.8-7v)/(2180)	\frac{dv}{dt}=\frac{457.8-7v}{2180}
e^{-3x}(y+1)dy=xe^{3x}(1+y^3)dx	e^{-3x}(y+1)dy=xe^{3x}(1+y^{3})dx
tangent of (4x)/(x+3)	tangent\:\frac{4x}{x+3}
tangent of y= 2/(sqrt(x))	tangent\:y=\frac{2}{\sqrt{x}}
x(dy)/(dx)+22y= 1/x	x\frac{dy}{dx}+22y=\frac{1}{x}
derivative of (e^{2x}-e^x+1)/(e^x)	derivative\:\frac{e^{2x}-e^{x}+1}{e^{x}}
e^x(dy)/(dx)+3e^xy=2	e^{x}\frac{dy}{dx}+3e^{x}y=2
limit as θ approaches 0 of cot(piθ)	\lim\:_{θ\to\:0}(\cot(πθ))
limit as x approaches 8 of (f(x))/(g(x))	\lim\:_{x\to\:8}(\frac{f(x)}{g(x)})
derivative of 4/(1-9x)	\frac{d}{dx}(\frac{4}{1-9x})
derivative of-x/3	derivative\:-\frac{x}{3}
derivative of-y/(x^2+y^2)	\frac{d}{dx}(-\frac{y}{x^{2}+y^{2}})
derivative of e^{ax}sin(bx)	\frac{d}{dx}(e^{ax}\sin(bx))
x^2(dy)/(dx)=1-x^2+y^2-x^2y^2	x^{2}\frac{dy}{dx}=1-x^{2}+y^{2}-x^{2}y^{2}
integral of (x-a)^2	\int\:(x-a)^{2}dx
integral of (x^2+1)/((x^2-2x+2)^2)	\int\:\frac{x^{2}+1}{(x^{2}-2x+2)^{2}}dx
derivative of (x-13)/(sqrt(x)-\sqrt{13)}	derivative\:\frac{x-13}{\sqrt{x}-\sqrt{13}}
(6x+1)y^2(dy)/(dx)+4x^2+2y^3=0	(6x+1)y^{2}\frac{dy}{dx}+4x^{2}+2y^{3}=0
(\partial)/(\partial x)(yx^2z^2-xy^4+xz)	\frac{\partial\:}{\partial\:x}(yx^{2}z^{2}-xy^{4}+xz)

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