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Popular Calculus Problems

integral of-6x	\int\:-6xdx
(\partial)/(\partial x)(1/(sin(x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sin(x)})
(\partial)/(\partial y)(3x-x^2y^2+2x^3y)	\frac{\partial\:}{\partial\:y}(3x-x^{2}y^{2}+2x^{3}y)
integral of 1/(3+4x^2)	\int\:\frac{1}{3+4x^{2}}dx
derivative of y=e^{x+2}	derivative\:y=e^{x+2}
sum from n=4 to infinity of (3/4)^{-n}	\sum\:_{n=4}^{\infty\:}(\frac{3}{4})^{-n}
(dy)/(dx)+y(x^2-1)+xy^6=0	\frac{dy}{dx}+y\cdot\:(x^{2}-1)+x\cdot\:y^{6}=0
derivative of (15x^7+27x^5/(3x))	\frac{d}{dx}(\frac{15x^{7}+27x^{5}}{3x})
y=x^{3x}	y=x^{3x}
derivative of x^2+y^2	derivative\:x^{2}+y^{2}
x(dy)/(dx)-3y=7x^4,y(1)=2	x\frac{dy}{dx}-3y=7x^{4},y(1)=2
tangent of f(x)= x/(x-3)	tangent\:f(x)=\frac{x}{x-3}
integral of ln(x^2-x-6)	\int\:\ln(x^{2}-x-6)dx
limit as x approaches 4+of x+sqrt(x-4)	\lim\:_{x\to\:4+}(x+\sqrt{x-4})
derivative of 2^{3x-4}	derivative\:2^{3x-4}
laplacetransform t-1	laplacetransform\:t-1
limit as p approaches infinity of (sqrt(p+1\sqrt{p+1)})/(sqrt(p+1))	\lim\:_{p\to\:\infty\:}(\frac{\sqrt{p+1\sqrt{p+1}}}{\sqrt{p+1}})
derivative of (e^{6x}/(x^2+5))	\frac{d}{dx}(\frac{e^{6x}}{x^{2}+5})
derivative of f(t)=(2t-1)^7+14t(2t-1)^6	derivative\:f(t)=(2t-1)^{7}+14t(2t-1)^{6}
y^'=(x+y-4)^2,y(0)=0	y^{\prime\:}=(x+y-4)^{2},y(0)=0
inverse oflaplace (10)/((2s+3))	inverselaplace\:\frac{10}{(2s+3)}
simplify (x^4)/4+1/(8x^2)	simplify\:\frac{x^{4}}{4}+\frac{1}{8x^{2}}
derivative of (x^2-x+1^{-7})	\frac{d}{dx}((x^{2}-x+1)^{-7})
integral of e^{-3x}sin(3x)	\int\:e^{-3x}\sin(3x)dx
(\partial)/(\partial y)(sin(x-y))	\frac{\partial\:}{\partial\:y}(\sin(x-y))
derivative of 2x^2-4x+6	\frac{d}{dx}(2x^{2}-4x+6)
derivative of y=-3-2e^x	derivative\:y=-3-2e^{x}
integral of ln((2x)^2)	\int\:\ln((2x)^{2})dx
integral of 1/(7x^2-14x+28)	\int\:\frac{1}{7x^{2}-14x+28}dx
derivative of y= 4/(x-2)	derivative\:y=\frac{4}{x-2}
integral of e^{sin(t)}cos(t)	\int\:e^{\sin(t)}\cos(t)dt
integral of 7x+3	\int\:7x+3dx
sum from n=1 to infinity}(n^2x^{4n of)/(5^{4n)}	\sum\:_{n=1}^{\infty\:}\frac{n^{2}x^{4n}}{5^{4n}}
integral of ((sqrt(x)+4)^4)/(2sqrt(x))	\int\:\frac{(\sqrt{x}+4)^{4}}{2\sqrt{x}}dx
limit as x approaches-0+of 1/(3x)	\lim\:_{x\to\:-0+}(\frac{1}{3x})
derivative of (3x^2-13^3)	\frac{d}{dx}((3x^{2}-13)^{3})
integral of-2pitan^5(pix)sec^3(pix)	\int\:-2π\tan^{5}(πx)\sec^{3}(πx)dx
derivative of y=-tcos(t)-t	derivative\:y=-t\cos(t)-t
derivative of sin(xln(sec(x)+tan(x))-1)	\frac{d}{dx}(\sin(x)\ln(\sec(x)+\tan(x))-1)
integral from-2 to 2 of 1/(y^2-9)	\int\:_{-2}^{2}\frac{1}{y^{2}-9}dy
derivative of (sin(x)/(y^2))	\frac{d}{dx}(\frac{\sin(x)}{y^{2}})
derivative of 1/(2sqrt(x))+1/(5x^{4/5)}	derivative\:\frac{1}{2\sqrt{x}}+\frac{1}{5x^{\frac{4}{5}}}
integral from 0 to 1 of t/(t^2+1)	\int\:_{0}^{1}\frac{t}{t^{2}+1}dt
derivative of 3*ln(x)	\frac{d}{dx}(3\cdot\:\ln(x))
derivative of-7sqrt(x)	\frac{d}{dx}(-7\sqrt{x})
(\partial)/(\partial v)(uv-v)	\frac{\partial\:}{\partial\:v}(uv-v)
laplacetransform (1+e^{2t})^2	laplacetransform\:(1+e^{2t})^{2}
integral of x^2cosh(mx)	\int\:x^{2}\cosh(mx)dx
(\partial)/(\partial x)(2x^4y^5+3x^3y^5)	\frac{\partial\:}{\partial\:x}(2x^{4}y^{5}+3x^{3}y^{5})
2y^{''}+12y^'+50y=0	2y^{\prime\:\prime\:}+12y^{\prime\:}+50y=0
derivative of-(13)/(s^6)	derivative\:-\frac{13}{s^{6}}
integral of e^{5θ}	\int\:e^{5θ}dθ
integral of-cos^2(2x)	\int\:-\cos^{2}(2x)dx
y^'+t^2=0	y^{\prime\:}+t^{2}=0
integral of cos^2(2x)sin(2x)	\int\:\cos^{2}(2x)\sin(2x)dx
(dy)/(dx)=-(y^2)/(1+y^2)e^{-x}	\frac{dy}{dx}=-\frac{y^{2}}{1+y^{2}}e^{-x}
d/(dt)(3-t)	\frac{d}{dt}(3-t)
limit as x approaches 1+of sqrt(1-x^2)	\lim\:_{x\to\:1+}(\sqrt{1-x^{2}})
integral from 1/7 to 3 of 6xln(7x)	\int\:_{\frac{1}{7}}^{3}6x\ln(7x)dx
derivative of 3e^x+x	derivative\:3e^{x}+x
(d^2y)/(dx^2)-8x^2=0	\frac{d^{2}y}{dx^{2}}-8x^{2}=0
t*(dy)/(dt)=t^3+13t^3y	t\cdot\:\frac{dy}{dt}=t^{3}+13t^{3}y
integral of e^xcos(2e^x)	\int\:e^{x}\cos(2e^{x})dx
(d^2)/(dx^2)(x^9e^x)	\frac{d^{2}}{dx^{2}}(x^{9}e^{x})
integral of 5tsin^2(t)	\int\:5t\sin^{2}(t)dt
integral of 12x^2+6x-5	\int\:12x^{2}+6x-5dx
integral from 0 to pi/4 of tan^8(θ)sec^2(θ)	\int\:_{0}^{\frac{π}{4}}\tan^{8}(θ)\sec^{2}(θ)dθ
derivative of (e^x)/(ln(x))	derivative\:\frac{e^{x}}{\ln(x)}
derivative of xt	\frac{d}{dx}(xt)
limit as x approaches-2-of 1/(x-2)	\lim\:_{x\to\:-2-}(\frac{1}{x-2})
derivative of (3x^4-4(3-2x^3))	\frac{d}{dx}((3x^{4}-4)(3-2x^{3}))
integral of x^2sqrt(1+x)	\int\:x^{2}\sqrt{1+x}dx
derivative of y=xcos(x)sin(x)	derivative\:y=x\cos(x)\sin(x)
(\partial)/(\partial y)(4y(1/x-ln(x)))	\frac{\partial\:}{\partial\:y}(4y(\frac{1}{x}-\ln(x)))
integral from 0 to 9 of 1/(sqrt(x))	\int\:_{0}^{9}\frac{1}{\sqrt{x}}dx
area 3x^2,18x-21	area\:3x^{2},18x-21
derivative of y=sec(x)tan(x)	derivative\:y=\sec(x)\tan(x)
integral of 7e^{3x}	\int\:7e^{3x}dx
area sqrt(x-1),y=0,x=6	area\:\sqrt{x-1},y=0,x=6
f(t)=4e^{t/2}	f(t)=4e^{\frac{t}{2}}
tangent of f(x)=x^2-5,\at x=3	tangent\:f(x)=x^{2}-5,\at\:x=3
(\partial)/(\partial y)(2/(2x+3y))	\frac{\partial\:}{\partial\:y}(\frac{2}{2x+3y})
derivative of f(x)=x^2sin(x)	derivative\:f(x)=x^{2}\sin(x)
laplacetransform-3cos(t)	laplacetransform\:-3\cos(t)
integral of ((2x)/(x^2+y^4))	\int\:(\frac{2x}{x^{2}+y^{4}})dx
derivative of sqrt(x^3+x)	\frac{d}{dx}(\sqrt{x^{3}+x})
integral of 5cos^2(x)	\int\:5\cos^{2}(x)dx
derivative of-x^3+9x^2-6x+9	\frac{d}{dx}(-x^{3}+9x^{2}-6x+9)
derivative of 8/(sqrt(64+64t^2))	derivative\:\frac{8}{\sqrt{64+64t^{2}}}
(dy)/(dx)=2cos(x)(y+1),y(pi/6)=2	\frac{dy}{dx}=2\cos(x)(y+1),y(\frac{π}{6})=2
limit as x approaches 0+of (5x)^{3x}	\lim\:_{x\to\:0+}((5x)^{3x})
x^2y^'=2xy+y^2	x^{2}y^{\prime\:}=2xy+y^{2}
(\partial)/(\partial x)(2x^2y^2)	\frac{\partial\:}{\partial\:x}(2x^{2}y^{2})
sum from n=0 to infinity of 9(3/4)^n	\sum\:_{n=0}^{\infty\:}9(\frac{3}{4})^{n}
area y=x,0,4	area\:y=x,0,4
limit as x approaches infinity of 4x	\lim\:_{x\to\:\infty\:}(4x)
limit as x approaches 0 of ((e^x-e^{-x}-2sin(x)))/(3x^3)	\lim\:_{x\to\:0}(\frac{(e^{x}-e^{-x}-2\sin(x))}{3x^{3}})
sum from n=1 to infinity of 1/(sqrt(n))	\sum\:_{n=1}^{\infty\:}\frac{1}{\sqrt{n}}
taylor \sqrt[3]{x},1	taylor\:\sqrt[3]{x},1
integral of-2y	\int\:-2ydy

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