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Popular Calculus Problems

integral of (xcos(x^2))/(sqrt(sin(x^2)))	\int\:\frac{x\cos(x^{2})}{\sqrt{\sin(x^{2})}}dx
y^{''}+2sqrt(6)y^'+6y=0	y^{\prime\:\prime\:}+2\sqrt{6}y^{\prime\:}+6y=0
integral from 0 to 1 of (e^{2x}-e^x)	\int\:_{0}^{1}(e^{2x}-e^{x})dx
y^{''}+64y^'=0	y^{\prime\:\prime\:}+64y^{\prime\:}=0
integral from 1 to 3 of (x^2+2x)	\int\:_{1}^{3}(x^{2}+2x)dx
y^'+x^2sec(y)=0	y^{\prime\:}+x^{2}\sec(y)=0
derivative of-5	derivative\:-5
integral of sqrt(50+25e^{10t)+25e^{-10t}}	\int\:\sqrt{50+25e^{10t}+25e^{-10t}}dt
integral of sec^5(x)	\int\:\sec^{5}(x)dx
integral of (x-1)/(x+4)	\int\:\frac{x-1}{x+4}dx
integral of (2x-4)/(x^3+4x^2)	\int\:\frac{2x-4}{x^{3}+4x^{2}}dx
derivative of 3x^{-5/3}	\frac{d}{dx}(3x^{-\frac{5}{3}})
derivative of cos(sin(2x))	\frac{d}{dx}(\cos(\sin(2x)))
derivative of acos(7x+bsin(7x))	\frac{d}{dx}(a\cos(7x)+b\sin(7x))
sum from n=1 to infinity}(2^{-n of)/(5^{-n)}	\sum\:_{n=1}^{\infty\:}\frac{2^{-n}}{5^{-n}}
derivative of 5x+3	\frac{d}{dx}(5x+3)
laplacetransform t^2e^t	laplacetransform\:t^{2}e^{t}
derivative of f(x)=((x^2-1))/((2x-3))	derivative\:f(x)=\frac{(x^{2}-1)}{(2x-3)}
limit as t approaches infinity of Q(t)+(100-Q(t))e^{-kt}	\lim\:_{t\to\:\infty\:}(Q(t)+(100-Q(t))e^{-kt})
derivative of g(t)=4t^{-1/8}+3ln(t)+ln(5)	derivative\:g(t)=4t^{-\frac{1}{8}}+3\ln(t)+\ln(5)
y^'=(x+y+1)^2	y^{\prime\:}=(x+y+1)^{2}
integral of sec^2(θ)tan^3(θ)	\int\:\sec^{2}(θ)\tan^{3}(θ)dθ
derivative of x^{(1/5 ln(x)})	\frac{d}{dx}(x^{(\frac{1}{5}\ln(x))})
derivative of sin(1/x)	derivative\:\sin(\frac{1}{x})
integral of sqrt(x+6)	\int\:\sqrt{x+6}dx
area y=x,y=2x,y=-x+4	area\:y=x,y=2x,y=-x+4
limit as x approaches 1 of 2(0.9)+1	\lim\:_{x\to\:1}(2(0.9)+1)
(\partial)/(\partial x)(-3e^{-3x})	\frac{\partial\:}{\partial\:x}(-3e^{-3x})
sum from n=1 to infinity of 1/(1.05^n)*1	\sum\:_{n=1}^{\infty\:}\frac{1}{1.05^{n}}\cdot\:1
integral from 6 to infinity of xe^{-5x}	\int\:_{6}^{\infty\:}xe^{-5x}dx
derivative of 2ln(3x^2-1)	\frac{d}{dx}(2\ln(3x^{2}-1))
derivative of-19x^2+4x+22	\frac{d}{dx}(-19x^{2}+4x+22)
derivative of g(x)=x^5-2x	derivative\:g(x)=x^{5}-2x
integral of 1/(x^2-x+6)	\int\:\frac{1}{x^{2}-x+6}dx
integral of e^{-xy}	\int\:e^{-xy}dy
integral of (csc(x))^2	\int\:(\csc(x))^{2}dx
integral of (-10x^2)/(sqrt(4x-x^2))	\int\:\frac{-10x^{2}}{\sqrt{4x-x^{2}}}dx
derivative of (x^3/(19))	\frac{d}{dx}(\frac{x^{3}}{19})
derivative of 6/(x^{-3})	\frac{d}{dx}(\frac{6}{x^{-3}})
y^{''}=-3y-2y^'	y^{\prime\:\prime\:}=-3y-2y^{\prime\:}
derivative of 5/(e^x)	derivative\:\frac{5}{e^{x}}
derivative of (t-sqrt(t))/(t^{1/4)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{4}}}
derivative of f(1/2)=10+12x-3x^2-x^3	derivative\:f(\frac{1}{2})=10+12x-3x^{2}-x^{3}
limit as x approaches 1 of (x^{3a}-3ax+3a-1)/((x-1)^2)	\lim\:_{x\to\:1}(\frac{x^{3a}-3ax+3a-1}{(x-1)^{2}})
derivative of ln^3(sec(2^{\sqrt[3]{x}}))	\frac{d}{dx}(\ln^{3}(\sec(2^{\sqrt[3]{x}})))
d/(dt)(4t^2+3t-10)	\frac{d}{dt}(4t^{2}+3t-10)
derivative of 13e^{x^2}	derivative\:13e^{x^{2}}
y^'+3y=4	y^{\prime\:}+3y=4
-y^'x+y=-7x	-y^{\prime\:}x+y=-7x
derivative of (x-2(x-3)^2)	\frac{d}{dx}((x-2)(x-3)^{2})
integral from 0 to pi/6 of 3sec^2(x)	\int\:_{0}^{\frac{π}{6}}3\sec^{2}(x)dx
integral of cos^3(1/3)x	\int\:\cos^{3}(\frac{1}{3})xdx
(dy)/(dx)+1/x y=3cos(2x)	\frac{dy}{dx}+\frac{1}{x}y=3\cos(2x)
integral of 1/(1+sqrt(7x))	\int\:\frac{1}{1+\sqrt{7x}}dx
(\partial)/(\partial x)(sqrt(x^2+y^2-2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}-2})
(\partial)/(\partial x)(ln(6ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(6ye^{xy}))
integral of (8+pi)	\int\:(8+π)dx
derivative of (1+arccos(3x)^3)	\frac{d}{dx}((1+\arccos(3x))^{3})
integral of \|2x\|	\int\:\left\|2x\right\|dx
tangent of f(x)=3x^5e^{2x}	tangent\:f(x)=3x^{5}e^{2x}
limit as x approaches 0 of 1/(x+1)-1	\lim\:_{x\to\:0}(\frac{1}{x+1}-1)
derivative of e^{-0.5}(2x+1)^{0.5}	derivative\:e^{-0.5}(2x+1)^{0.5}
integral of cos^3(xsi)n^5x	\int\:\cos^{3}(xsi)n^{5}xdx
y^{''}+25y=cos(2t)	y^{\prime\:\prime\:}+25y=\cos(2t)
integral of (2+7x)/(1+x^2)	\int\:\frac{2+7x}{1+x^{2}}dx
integral from 0 to pi/2 of 9cos^2(x)	\int\:_{0}^{\frac{π}{2}}9\cos^{2}(x)dx
integral of e^xsqrt(4-e^x)	\int\:e^{x}\sqrt{4-e^{x}}dx
area 6-x,sqrt(x),1	area\:6-x,\sqrt{x},1
derivative of (8x/(7-cot(x)))	\frac{d}{dx}(\frac{8x}{7-\cot(x)})
area xln(x),-x+1,[1,3]	area\:x\ln(x),-x+1,[1,3]
y^{''}+9y=te^{2t}	y^{\prime\:\prime\:}+9y=te^{2t}
derivative of x^9ln(4x)	\frac{d}{dx}(x^{9}\ln(4x))
d/(dt)(3)	\frac{d}{dt}(3)
derivative of f(x)=ln(4)	derivative\:f(x)=\ln(4)
derivative of \sqrt[5]{(5x/(3x-2)})	\frac{d}{dx}(\sqrt[5]{\frac{5x}{3x-2}})
xdx+(x^2y+4y)dy=0,y(4)=0	xdx+(x^{2}y+4y)dy=0,y(4)=0
derivative of (\sqrt[3]{x}/5)	\frac{d}{dx}(\frac{\sqrt[3]{x}}{5})
tangent of f(x)=3ln(x^5),\at (15)/e	tangent\:f(x)=3\ln(x^{5}),\at\:\frac{15}{e}
integral of x^2+1/(x^2)	\int\:x^{2}+\frac{1}{x^{2}}dx
integral of (x+1)sin(5x)	\int\:(x+1)\sin(5x)dx
(dy)/(dx)=(cos(20x))/(e^{20y)},y(0)=2	\frac{dy}{dx}=\frac{\cos(20x)}{e^{20y}},y(0)=2
integral of x^2cos(x	\int\:x^{2}\cos(d)xdx
integral of (cot(x/2))/(sin(x))	\int\:\frac{\cot(\frac{x}{2})}{\sin(x)}dx
derivative of f(x)=8(4e^x-26)^4	derivative\:f(x)=8(4e^{x}-26)^{4}
limit as x approaches 0 of (x-2)^5	\lim\:_{x\to\:0}((x-2)^{5})
inverse oflaplace 1/(s*(s+2))	inverselaplace\:\frac{1}{s\cdot\:(s+2)}
limit as x approaches 0 of (x^3)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{3}}{x^{2}})
integral of (cos(x)-1)/(x^2)	\int\:\frac{\cos(x)-1}{x^{2}}dx
integral of (cos(x))/(sin^2(x)-2)	\int\:\frac{\cos(x)}{\sin^{2}(x)-2}dx
sum from n=1 to infinity of 1/((n^2+1))	\sum\:_{n=1}^{\infty\:}\frac{1}{(n^{2}+1)}
limit as x approaches 0+of x^{-(17)/(ln(x))}	\lim\:_{x\to\:0+}(x^{-\frac{17}{\ln(x)}})
(dy)/(dx)=3x(e^{2y})	\frac{dy}{dx}=3x(e^{2y})
derivative of (3x+3/(4e^x))	\frac{d}{dx}(\frac{3x+3}{4e^{x}})
integral of (2x+1)/(x+2)	\int\:\frac{2x+1}{x+2}dx
(dy)/(dx)=(y+5)(x-2)	\frac{dy}{dx}=(y+5)(x-2)
derivative of 2^{sin(x}*ta{g}(x,t)(x-x^3))	\frac{d}{dx}(2^{\sin(x)}\cdot\:ta{g}(x,t)(x-x^{3}))
integral of (x-1)/(x^3+x)	\int\:\frac{x-1}{x^{3}+x}dx
f(x)=xe^{4x}	f(x)=xe^{4x}
integral of 4csc(x)cot(x)+2sec^2(x)	\int\:4\csc(x)\cot(x)+2\sec^{2}(x)dx
(\partial)/(\partial y)(5e^xln(y))	\frac{\partial\:}{\partial\:y}(5e^{x}\ln(y))

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