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Popular Calculus Problems

integral from t-1 to 2 of-t+2	\int\:_{t-1}^{2}-t+2dt
derivative of f(x)=(2x+3)^3	derivative\:f(x)=(2x+3)^{3}
derivative of 1+3x	\frac{d}{dx}(1+3x)
integral of (x^2-2x+1)e^{2x}	\int\:(x^{2}-2x+1)e^{2x}dx
limit as x approaches pi of 2cot(x)	\lim\:_{x\to\:π}(2\cot(x))
integral of e^{t^3}	\int\:e^{t^{3}}dt
integral of 7cos(sqrt(4x))	\int\:7\cos(\sqrt{4x})dx
f(x)=3x^4-7ln(x)	f(x)=3x^{4}-7\ln(x)
integral of 2\sqrt[3]{x}	\int\:2\sqrt[3]{x}dx
(\partial)/(\partial y)(y^2+x)	\frac{\partial\:}{\partial\:y}(y^{2}+x)
inverse oflaplace 1/s-s/(s^2+1)	inverselaplace\:\frac{1}{s}-\frac{s}{s^{2}+1}
integral of 1/(2sqrt(3-x)\sqrt{x+1)}	\int\:\frac{1}{2\sqrt{3-x}\sqrt{x+1}}dx
derivative of ln(x^2e^x)	\frac{d}{dx}(\ln(x^{2}e^{x}))
sum from n=0 to infinity of 1/((n^3-n))	\sum\:_{n=0}^{\infty\:}\frac{1}{(n^{3}-n)}
y^'+8x-1y=x^8,y(1)=9	y^{\prime\:}+8x-1y=x^{8},y(1)=9
derivative of psqrt(p)	derivative\:p\sqrt{p}
integral of ((3x+1)^2)/(244)	\int\:\frac{(3x+1)^{2}}{244}dx
d/(dθ)(sin(θ)+θcos(θ))	\frac{d}{dθ}(\sin(θ)+θ\cos(θ))
(\partial)/(\partial x)(2sin(3x+2y))	\frac{\partial\:}{\partial\:x}(2\sin(3x+2y))
integral of (sqrt(y+1))/y	\int\:\frac{\sqrt{y+1}}{y}dy
derivative of e^xcos(x^2)	\frac{d}{dx}(e^{x}\cos(x^{2}))
limit as y approaches-1 of-y^5-3y^4	\lim\:_{y\to\:-1}(-y^{5}-3y^{4})
tangent of f(x)=e^{2x},(0,1)	tangent\:f(x)=e^{2x},(0,1)
sum from n=1 to infinity of (-1)^nn^{-1}	\sum\:_{n=1}^{\infty\:}(-1)^{n}n^{-1}
y^{''}+5y^'=e^{-t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+5y^{\prime\:}=e^{-t},y(0)=0,y^{\prime\:}(0)=0
(\partial)/(\partial z)(e^x+yz)	\frac{\partial\:}{\partial\:z}(e^{x}+yz)
simplify sqrt(f(x))	simplify\:\sqrt{f(x)}
limit as x approaches 6+of x/(36-x^2)	\lim\:_{x\to\:6+}(\frac{x}{36-x^{2}})
derivative of 2xarcsin(x)	\frac{d}{dx}(2x\arcsin(x))
limit as x approaches 2 of [x]	\lim\:_{x\to\:2}([x])
derivative of (2x^3+x^2-2x/(x^4-2x^2-4))	\frac{d}{dx}(\frac{2x^{3}+x^{2}-2x}{x^{4}-2x^{2}-4})
derivative of x^2log_{e}(2x)	\frac{d}{dx}(x^{2}\log_{e}(2x))
(dy)/(dx)+4tan(4x)y=3cos(4x)	\frac{dy}{dx}+4\tan(4x)y=3\cos(4x)
slope of (0,1),(4,-5)	slope\:(0,1),(4,-5)
derivative of (1+x^2)/((1-x^2)^2)	derivative\:\frac{1+x^{2}}{(1-x^{2})^{2}}
derivative of (2-x/(x+4))	\frac{d}{dx}(\frac{2-x}{x+4})
(\partial)/(\partial y)(-xy^2z+4xy)	\frac{\partial\:}{\partial\:y}(-xy^{2}z+4xy)
(\partial)/(\partial x)(sin(x+y)+(x+y))	\frac{\partial\:}{\partial\:x}(\sin(x+y)+(x+y))
integral of 3/(x^3+x)	\int\:\frac{3}{x^{3}+x}dx
integral from 0 to 2 of te^{2t}	\int\:_{0}^{2}te^{2t}dt
(\partial)/(\partial x)(x^2e^{3xy})	\frac{\partial\:}{\partial\:x}(x^{2}e^{3xy})
integral of (x/(xsqrt(x^2+36)))	\int\:(\frac{x}{x\sqrt{x^{2}+36}})dx
(\partial)/(\partial y)(ln(x+y^2))	\frac{\partial\:}{\partial\:y}(\ln(x+y^{2}))
integral from 0 to 5 of 1/(x^{20/21)}	\int\:_{0}^{5}\frac{1}{x^{\frac{20}{21}}}dx
integral of ((x^2-1))/(x^2)	\int\:\frac{(x^{2}-1)}{x^{2}}dx
integral of (e^{2x})/(e^{2x)+3e^x+2}	\int\:\frac{e^{2x}}{e^{2x}+3e^{x}+2}dx
(\partial)/(\partial x)((e^{xy})/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{e^{xy}}{x+y})
derivative of \sqrt[3]{(8x^2-3/(x^2+2)})	\frac{d}{dx}(\sqrt[3]{\frac{8x^{2}-3}{x^{2}+2}})
integral of (e^3)/x	\int\:\frac{e^{3}}{x}dx
limit as x approaches 0 of (\|x\|)/(4x)	\lim\:_{x\to\:0}(\frac{\left\|x\right\|}{4x})
(d^2y)/(dx^2)-12(dy)/(dx)+36y=0	\frac{d^{2}y}{dx^{2}}-12\frac{dy}{dx}+36y=0
integral of tan(t/2)	\int\:\tan(\frac{t}{2})dt
integral from 0 to 1 of (x+7)(x-8)	\int\:_{0}^{1}(x+7)(x-8)dx
limit as x approaches-4 of-x^2+2x-8	\lim\:_{x\to\:-4}(-x^{2}+2x-8)
derivative of 5(e^x)^{-4}	derivative\:5(e^{x})^{-4}
(\partial)/(\partial w)(ve^w)	\frac{\partial\:}{\partial\:w}(ve^{w})
derivative of (x+1/x ^{10})	\frac{d}{dx}((x+\frac{1}{x})^{10})
integral of 2sin(x)e^x	\int\:2\sin(x)e^{x}dx
derivative of 3ae^{3x}	\frac{d}{dx}(3ae^{3x})
derivative of f(x)=1+x	derivative\:f(x)=1+x
area y^2=2x+1,y=x-1	area\:y^{2}=2x+1,y=x-1
integral of cos(Inx)	\int\:\cos(Inx)dx
y^'+y=e^{(-t)}	y^{\prime\:}+y=e^{(-t)}
integral of 1/((x+3)(x-3))	\int\:\frac{1}{(x+3)(x-3)}dx
derivative of x-3sin(x)	\frac{d}{dx}(x-3\sin(x))
integral of (e^u)/((4-e^u)^2)	\int\:\frac{e^{u}}{(4-e^{u})^{2}}du
(dy)/(dx)=y^2e^{-x}	\frac{dy}{dx}=y^{2}e^{-x}
integral of x*x^{20}	\int\:x\cdot\:x^{20}dx
laplacetransform t^2e^{-2t}	laplacetransform\:t^{2}e^{-2t}
limit as x approaches 0 of e^0cos(4)(0)	\lim\:_{x\to\:0}(e^{0}\cos(4)(0))
limit as x approaches 3 of 4e^{x-3}	\lim\:_{x\to\:3}(4e^{x-3})
y^'=e^{2x}(1+y^2)	y^{\prime\:}=e^{2x}(1+y^{2})
integral of y^2-2x	\int\:y^{2}-2xdx
integral of xe^{-8x}	\int\:xe^{-8x}dx
integral of \sqrt[3]{x}ln(x^5)	\int\:\sqrt[3]{x}\ln(x^{5})dx
limit as x approaches-infinity of x+1	\lim\:_{x\to\:-\infty\:}(x+1)
derivative of 3x^4+2x^{1/3}-1/(x^2)	\frac{d}{dx}(3x^{4}+2x^{\frac{1}{3}}-\frac{1}{x^{2}})
integral of (-11x-24)/(125(x^2+4x+5))	\int\:\frac{-11x-24}{125(x^{2}+4x+5)}dx
sum from n=1 to infinity of 2/(5^{n+2)}	\sum\:_{n=1}^{\infty\:}\frac{2}{5^{n+2}}
derivative of (e^{x^2}+3e^x/(e^x))	\frac{d}{dx}(\frac{e^{x^{2}}+3e^{x}}{e^{x}})
integral of 12\sqrt[3]{81-9x}-36	\int\:12\sqrt[3]{81-9x}-36dx
integral of (ln(t))/(t^3)	\int\:\frac{\ln(t)}{t^{3}}dt
limit as x approaches 3-of 2/(x^2-9)	\lim\:_{x\to\:3-}(\frac{2}{x^{2}-9})
derivative of e^{9-x}	derivative\:e^{9-x}
y^{''}+25y=cos(6t)	y^{\prime\:\prime\:}+25y=\cos(6t)
integral of (1/(sin^2(x)))	\int\:(\frac{1}{\sin^{2}(x)})dx
integral of (5x^2)/((x-1)(x^2+9))	\int\:\frac{5x^{2}}{(x-1)(x^{2}+9)}dx
limit as x approaches 3 of x^2-5x	\lim\:_{x\to\:3}(x^{2}-5x)
d/(ds)(s^2{y}(s)-1)	\frac{d}{ds}(s^{2}{y}(s)-1)
derivative of f(x)=x^2-2x+1	derivative\:f(x)=x^{2}-2x+1
derivative of 6sqrt(t)-2/(sqrt(t))	derivative\:6\sqrt{t}-\frac{2}{\sqrt{t}}
derivative of 1/3 x^3-1/2 x^2-6x	\frac{d}{dx}(\frac{1}{3}x^{3}-\frac{1}{2}x^{2}-6x)
inverse oflaplace (3s+17)/(s^2+s+1)	inverselaplace\:\frac{3s+17}{s^{2}+s+1}
t^2y^{''}+19ty^'+106y=0	t^{2}y^{\prime\:\prime\:}+19ty^{\prime\:}+106y=0
limit as x approaches 0 of tan(1/x)	\lim\:_{x\to\:0}(\tan(\frac{1}{x}))
tangent of f(x)=x^{-2},\at x=-2	tangent\:f(x)=x^{-2},\at\:x=-2
(\partial)/(\partial p)(((p+q))/(p+r))	\frac{\partial\:}{\partial\:p}(\frac{(p+q)}{p+r})
limit as x approaches 0 of (sin(4x))/(cos(5x))	\lim\:_{x\to\:0}(\frac{\sin(4x)}{\cos(5x)})
derivative of-3x^3+2x^2+5x-2	\frac{d}{dx}(-3x^{3}+2x^{2}+5x-2)
limit as x approaches 0 of (x^2)sin(1/x)	\lim\:_{x\to\:0}((x^{2})\sin(\frac{1}{x}))

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