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Popular Calculus Problems

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
integral of t^8e^{-t^9}	\int\:t^{8}e^{-t^{9}}dt
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})
limit as t approaches 0 of e^{2t}	\lim\:_{t\to\:0}(e^{2t})
derivative of x^2-sin^2(x)	\frac{d}{dx}(x^{2}-\sin^{2}(x))
y^'=e^{2x}(1+y^2)	y^{\prime\:}=e^{2x}(1+y^{2})
derivative of xcos(x+3pi)	\frac{d}{dx}(x\cos(x)+3π)
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)
area 3x^3-x^2-10x,-x^2+2x	area\:3x^{3}-x^{2}-10x,-x^{2}+2x
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 (5x)/(sqrt(2-x^4))	\int\:\frac{5x}{\sqrt{2-x^{4}}}dx
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
integral of sech^2(x)tanh(x)	\int\:\sech^{2}(x)\tanh(x)dx
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 e^{-0.4x}	\frac{d}{dx}(e^{-0.4x})
derivative of \sqrt[3]{(4x^3+2x^5})	\frac{d}{dx}(\sqrt[3]{(4x^{3}+2x)^{5}})
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}
integral of (x^2-7)^4(2x)	\int\:(x^{2}-7)^{4}(2x)dx
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}))
integral of (x^2+x+1)/(x^3+2x^2)	\int\:\frac{x^{2}+x+1}{x^{3}+2x^{2}}dx
(\partial)/(\partial y)(xe^xcos(y))	\frac{\partial\:}{\partial\:y}(xe^{x}\cos(y))
f(x)=2sin(2x)-ln(3x+1)	f(x)=2\sin(2x)-\ln(3x+1)
integral of cos(x)-cos^2(x)	\int\:\cos(x)-\cos^{2}(x)dx
integral from 2 to 4 of 2pix(-3/2 x+6)	\int\:_{2}^{4}2πx(-\frac{3}{2}x+6)dx
integral of x/2 e^{-x/2}	\int\:\frac{x}{2}e^{-\frac{x}{2}}dx
(1+x^2)*(dy)/(dx)-(4x^3y)/(1-x^2)=1	(1+x^{2})\cdot\:\frac{dy}{dx}-\frac{4x^{3}y}{1-x^{2}}=1
integral from 0 to 1 of (15sqrt(5x+4))/2	\int\:_{0}^{1}\frac{15\sqrt{5x+4}}{2}dx
(dy)/(dx)-7y=e^x	\frac{dy}{dx}-7y=e^{x}
y^'=(11x^2-1)/(11+4y)	y^{\prime\:}=\frac{11x^{2}-1}{11+4y}
derivative of h(t)=(t+1)^{2/3}(2t^2-5)^3	derivative\:h(t)=(t+1)^{\frac{2}{3}}(2t^{2}-5)^{3}
tangent of f(x)=(7x)/(3+x^2),\at x=2	tangent\:f(x)=\frac{7x}{3+x^{2}},\at\:x=2
limit as x approaches 1 of-1/((x-1)^2)	\lim\:_{x\to\:1}(-\frac{1}{(x-1)^{2}})
tangent of y=(-6x)/(x^2+1),(0,0)	tangent\:y=\frac{-6x}{x^{2}+1},(0,0)
derivative of f(x)=4x^2-x	derivative\:f(x)=4x^{2}-x
integral of 1/(9x)	\int\:\frac{1}{9x}dx
integral of (x^2)/(sqrt(x^2-4x+20))	\int\:\frac{x^{2}}{\sqrt{x^{2}-4x+20}}dx
area 7e^x,7xe^{x^2},1,7e	area\:7e^{x},7xe^{x^{2}},1,7e
tangent of f(x)= x/((1+x^2)),\at x=2	tangent\:f(x)=\frac{x}{(1+x^{2})},\at\:x=2
derivative of 3/(x^6-1/(x^4)+5)	\frac{d}{dx}(\frac{3}{x^{6}}-\frac{1}{x^{4}}+5)
derivative of f(x)=(3x^2+2)(8x^3-3)	derivative\:f(x)=(3x^{2}+2)(8x^{3}-3)
derivative of y=5e^x+8/(\sqrt[3]{x)}	derivative\:y=5e^{x}+\frac{8}{\sqrt[3]{x}}
(dy)/(dx)=5yx	\frac{dy}{dx}=5yx
integral of (30)/((x+1)(x^2+9)^2)	\int\:\frac{30}{(x+1)(x^{2}+9)^{2}}dx
integral of sqrt(8-x^2)	\int\:\sqrt{8-x^{2}}dx
limit as x approaches 1 of 3x^2+3x-1	\lim\:_{x\to\:1}(3x^{2}+3x-1)
integral of ln(x-4)	\int\:\ln(x-4)dx
derivative of (\sqrt[3]{x}/({f)(x)})	\frac{d}{dx}(\frac{\sqrt[3]{x}}{{f}(x)})
limit as x approaches 1+of x^{1/(x-1)}	\lim\:_{x\to\:1+}(x^{\frac{1}{x-1}})
implicit (dy)/(dx),xy=7	implicit\:\frac{dy}{dx},xy=7
integral of (2x^2)/(x^2-1)	\int\:\frac{2x^{2}}{x^{2}-1}dx
(dy)/(dx)=e^{4x}+9y	\frac{dy}{dx}=e^{4x}+9y
derivative of y= 1/(\sqrt[3]{e^x)}	derivative\:y=\frac{1}{\sqrt[3]{e^{x}}}
integral of 2x^4e^{x^5}	\int\:2x^{4}e^{x^{5}}dx
tangent of f(x)=x^2+6,\at x=-7	tangent\:f(x)=x^{2}+6,\at\:x=-7
integral from-2 to-1 of cos(npi/2x)	\int\:_{-2}^{-1}\cos(n\cdot\:\frac{π}{2}\cdot\:x)dx
limit as x approaches 4 of \sqrt[3]{x}	\lim\:_{x\to\:4}(\sqrt[3]{x})
limit as x approaches 5+of (x+2)/(5-x)	\lim\:_{x\to\:5+}(\frac{x+2}{5-x})
integral of 2xsin(x)e^x	\int\:2x\cdot\:\sin(x)\cdot\:e^{x}dx
integral of 1/(xsqrt(5+x^2))	\int\:\frac{1}{x\sqrt{5+x^{2}}}dx
derivative of 5xsin(4pix)	\frac{d}{dx}(5x\sin(4π)x)
integral of 3x^2y^{-2}+2xy^{-1}	\int\:3x^{2}y^{-2}+2xy^{-1}dx
integral of sin^4(1/2 x)cos^4(1/2 x)	\int\:\sin^{4}(\frac{1}{2}x)\cos^{4}(\frac{1}{2}x)dx
f(t)=4cos(t)	f(t)=4\cos(t)
(y^3-x^3)y^'(x)=3x^2y+1,y(-2)=-1	(y^{3}-x^{3})y^{\prime\:}(x)=3x^{2}y+1,y(-2)=-1
y^'=-(1+y)/(1+x+y)	y^{\prime\:}=-\frac{1+y}{1+x+y}
(dy)/(dx)=7y(7-y)	\frac{dy}{dx}=7y(7-y)
derivative of (5x^3+9x^2)/x	derivative\:\frac{5x^{3}+9x^{2}}{x}

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