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Popular Calculus Problems

integral of-2e^{2t}	\int\:-2e^{2t}dt
integral of 1/(1+17x)	\int\:\frac{1}{1+17x}dx
integral of (xsin(x))	\int\:(x\sin(x))dx
derivative of y=(2x)/(4+x^2)	derivative\:y=\frac{2x}{4+x^{2}}
(dx)/(dt)= 2/(sqrt(x))	\frac{dx}{dt}=\frac{2}{\sqrt{x}}
limit as x approaches 6 of (x+1)^2	\lim\:_{x\to\:6}((x+1)^{2})
integral of 1/((3x+5)^4)	\int\:\frac{1}{(3x+5)^{4}}dx
(\partial)/(\partial x)((x+2)^2)	\frac{\partial\:}{\partial\:x}((x+2)^{2})
integral from 27 to-1 of (-8\sqrt[3]{x})	\int\:_{27}^{-1}(-8\sqrt[3]{x})dx
y^'=3y+5	y^{\prime\:}=3y+5
integral of-10sin(x)	\int\:-10\sin(x)dx
limit as x approaches 6 of \sqrt[3]{x-6}	\lim\:_{x\to\:6}(\sqrt[3]{x-6})
area x=y^2-8,x=2y	area\:x=y^{2}-8,x=2y
derivative of (x-3/x+ln(x/3))	\frac{d}{dx}(\frac{x-3}{x}+\ln(\frac{x}{3}))
limit as x approaches infinity of 3ln(x)	\lim\:_{x\to\:\infty\:}(3\ln(x))
derivative of k	derivative\:k
integral from sqrt(2) to 2 of u/(u^2-1)	\int\:_{\sqrt{2}}^{2}\frac{u}{u^{2}-1}du
(\partial)/(\partial y)(e^{x+y+1})	\frac{\partial\:}{\partial\:y}(e^{x+y+1})
integral from 0 to 1 of x-x^2	\int\:_{0}^{1}x-x^{2}dx
area y=x^2+2x+1,y=2x+5	area\:y=x^{2}+2x+1,y=2x+5
(\partial)/(\partial x)(-6xy)	\frac{\partial\:}{\partial\:x}(-6xy)
derivative of 1/5 x^5+1/(12x^3)	\frac{d}{dx}(\frac{1}{5}x^{5}+\frac{1}{12x^{3}})
x^2y^'-2xy=sin(4x)x^4	x^{2}y^{\prime\:}-2xy=\sin(4x)x^{4}
maclaurin arctan(3x)	maclaurin\:\arctan(3x)
d/(dt)(sin^2(t))	\frac{d}{dt}(\sin^{2}(t))
derivative of 6e^x+2y	\frac{d}{dx}(6e^{x}+2y)
(2x-4)(dy)/(dx)-y^2=0	(2x-4)\frac{dy}{dx}-y^{2}=0
derivative of cos(xcos(x))	\frac{d}{dx}(\cos(x)\cos(x))
derivative of (x+8/(3x^2e^x))	\frac{d}{dx}(\frac{x+8}{3x^{2}e^{x}})
derivative of-(x^2/2+5x+3)	\frac{d}{dx}(-\frac{x^{2}}{2}+5x+3)
y^'=((x^2))/(y(1+x^3))	y^{\prime\:}=\frac{(x^{2})}{y(1+x^{3})}
integral from 0 to x of e^{-t}	\int\:_{0}^{x}e^{-t}dt
derivative of (x-x^3^x)	\frac{d}{dx}((x-x^{3})^{x})
limit as x approaches-infinity of-e^{-x}	\lim\:_{x\to\:-\infty\:}(-e^{-x})
integral of 12sin^2(t)cos(t)	\int\:12\sin^{2}(t)\cos(t)dt
integral of (12x+5)^2	\int\:(12x+5)^{2}dx
sum from n=1 to infinity of \sqrt[n]{6}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{6}
tangent of sin(9x)+cos(2x)	tangent\:\sin(9x)+\cos(2x)
derivative of y=(2x^4+1)^2	derivative\:y=(2x^{4}+1)^{2}
tangent of f(x)=(4x)/(x^2+1),(0,0)	tangent\:f(x)=\frac{4x}{x^{2}+1},(0,0)
integral from 1 to 3 of 1/((x-1)^{3/2)}	\int\:_{1}^{3}\frac{1}{(x-1)^{\frac{3}{2}}}dx
integral of 1/(2sin(x)+cos(x))	\int\:\frac{1}{2\sin(x)+\cos(x)}dx
y^'=2y+xe^x	y^{\prime\:}=2y+xe^{x}
limit as x approaches+0 of (ln(x))/x	\lim\:_{x\to\:+0}(\frac{\ln(x)}{x})
tangent of y=(1+4x)^8,(0,1)	tangent\:y=(1+4x)^{8},(0,1)
limit as x approaches 0+of inf(t,y,x)inity	\lim\:_{x\to\:0+}(inf(t,y,x)inity)
(dy)/(dx)+3y=3x^2e^{-3x}	\frac{dy}{dx}+3y=3x^{2}e^{-3x}
integral of (18)/(9x^2-x^4)	\int\:\frac{18}{9x^{2}-x^{4}}dx
limit as x approaches 0-of e^{x/(x+1)}	\lim\:_{x\to\:0-}(e^{\frac{x}{x+1}})
integral of (sqrt(1+x^2))/(x^2)	\int\:\frac{\sqrt{1+x^{2}}}{x^{2}}dx
integral of (x^3+x)/((x^2+3)(x^2-2x+3))	\int\:\frac{x^{3}+x}{(x^{2}+3)(x^{2}-2x+3)}dx
integral of e^{2x}sqrt(1+e^x)	\int\:e^{2x}\sqrt{1+e^{x}}dx
limit as x approaches 0 of (x-sin(x))/x	\lim\:_{x\to\:0}(\frac{x-\sin(x)}{x})
(\partial)/(\partial y)(ysin(y))	\frac{\partial\:}{\partial\:y}(y\sin(y))
derivative of y=8xsin(x^2)	derivative\:y=8x\sin(x^{2})
(\partial)/(\partial y)(7e^{7e^{yx}+y}x)	\frac{\partial\:}{\partial\:y}(7e^{7e^{yx}+y}x)
derivative of-4sin(2x+3cos(3x))	\frac{d}{dx}(-4\sin(2x)+3\cos(3x))
integral from 0 to 1 of 6e^{-4x}	\int\:_{0}^{1}6e^{-4x}dx
(dy)/(dx)+(2xy)/(1+x^2)=-2xy^2	\frac{dy}{dx}+\frac{2xy}{1+x^{2}}=-2xy^{2}
inverse oflaplace (28s)/((s^2+11))	inverselaplace\:\frac{28s}{(s^{2}+11)}
(dy)/(dx)+4tan(4x)(y)=3cos(4x)	\frac{dy}{dx}+4\tan(4x)(y)=3\cos(4x)
integral from-2 to 3 of (x^2+3x-13)	\int\:_{-2}^{3}(x^{2}+3x-13)dx
limit as x approaches 0 of arctan(ln(x))	\lim\:_{x\to\:0}(\arctan(\ln(x)))
(cos(x)sin(x))^'	(\cos(x)\sin(x))^{\prime\:}
(\partial)/(\partial x)(3xe^{-xy})	\frac{\partial\:}{\partial\:x}(3xe^{-xy})
inverse oflaplace e^{-2s} 1/(10s+2)	inverselaplace\:e^{-2s}\frac{1}{10s+2}
derivative of 2x^{3/2}+7	\frac{d}{dx}(2x^{\frac{3}{2}}+7)
integral of ((ln(x))^{11})/x	\int\:\frac{(\ln(x))^{11}}{x}dx
(arctan(sqrt(x)))^'	(\arctan(\sqrt{x}))^{\prime\:}
derivative of 8e^x+8/(\sqrt[3]{x})	\frac{d}{dx}(8e^{x}+\frac{8}{\sqrt[3]{x}})
integral of 5/(\sqrt[3]{x^2)}	\int\:\frac{5}{\sqrt[3]{x^{2}}}dx
integral of 4/((x+1)(x+3))	\int\:\frac{4}{(x+1)(x+3)}dx
limit as x approaches infinity of (8^x)/(9^{x+1)}	\lim\:_{x\to\:\infty\:}(\frac{8^{x}}{9^{x+1}})
integral of (32)/(1-cos(4x))	\int\:\frac{32}{1-\cos(4x)}dx
integral from 0 to 4 of x/(x^2-4)	\int\:_{0}^{4}\frac{x}{x^{2}-4}dx
(\partial)/(\partial x)(r(θ,x)cos(θ))	\frac{\partial\:}{\partial\:x}(r(θ,x)\cos(θ))
limit as x approaches 3-of 3/(x^2-9)	\lim\:_{x\to\:3-}(\frac{3}{x^{2}-9})
integral from 1 to 3 of (x^2+5)/(4x-x^2)	\int\:_{1}^{3}\frac{x^{2}+5}{4x-x^{2}}dx
derivative of (1/(1-x)^2)	\frac{d}{dx}((\frac{1}{1-x})^{2})
derivative of 15x^4	\frac{d}{dx}(15x^{4})
simplify 2/(sqrt(x))-1	simplify\:\frac{2}{\sqrt{x}}-1
integral of (arcsin(3x))/(sqrt(1-9x^2))	\int\:\frac{\arcsin(3x)}{\sqrt{1-9x^{2}}}dx
derivative of y=((x-1))/(x+1)	derivative\:y=\frac{(x-1)}{x+1}
integral of xysin(x^2y)	\int\:xy\sin(x^{2}y)dx
(\partial)/(\partial y)(2y^3)	\frac{\partial\:}{\partial\:y}(2y^{3})
integral of (16x^2)/((x-24)(x+8)^2)	\int\:\frac{16x^{2}}{(x-24)(x+8)^{2}}dx
integral from 0 to 1 of 2/(sqrt(1-x^2))	\int\:_{0}^{1}\frac{2}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial y)((x+1)/(y-1))	\frac{\partial\:}{\partial\:y}(\frac{x+1}{y-1})
integral from 0 to 1 of 1/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{1}{\sqrt{x}(1+x)}dx
integral of ysqrt(y+1)	\int\:y\sqrt{y+1}dy
derivative of y=5x-x^2	derivative\:y=5x-x^{2}
derivative of 4tan^2(3x)	derivative\:4\tan^{2}(3x)
integral of-ln(x)	\int\:-\ln(x)dx
(\partial)/(\partial y)(1/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}+y^{2}})
limit as n approaches infinity of an	\lim\:_{n\to\:\infty\:}(an)
limit as x approaches 3 of 7/(x-3)	\lim\:_{x\to\:3}(\frac{7}{x-3})
integral of-2/(sqrt(x))	\int\:-\frac{2}{\sqrt{x}}dx
(dy)/(dt)= 2/t y+3t^2cos(3t)	\frac{dy}{dt}=\frac{2}{t}y+3t^{2}\cos(3t)
integral from 1 to infinity of x^{-2/3}	\int\:_{1}^{\infty\:}x^{-\frac{2}{3}}dx
integral of (x^2+1)cos(x)	\int\:(x^{2}+1)\cos(x)dx

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