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Popular Calculus Problems
integral of 2/(e^x+e^{-x)}
\int\:\frac{2}{e^{x}+e^{-x}}dx
integral of 6cos(sqrt(8x))
\int\:6\cos(\sqrt{8x})dx
derivative of 1/z
derivative\:\frac{1}{z}
integral of (3x^2-2x+5)
\int\:(3x^{2}-2x+5)dx
domain of f(x)=-3/x
domain\:f(x)=-\frac{3}{x}
y^{''}-5y^'+6y=cos(x)e^{-x}
y^{\prime\:\prime\:}-5y^{\prime\:}+6y=\cos(x)e^{-x}
integral of (sin(2x))/(32+cos^2(x))
\int\:\frac{\sin(2x)}{32+\cos^{2}(x)}dx
(dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200
\frac{dP}{dt}=0.16P(1-\frac{P}{1000})-30,P(0)=200
derivative of 6cos(t)-2sin(t)
derivative\:6\cos(t)-2\sin(t)
slope of f(t)=t^3-27t+5
slope\:f(t)=t^{3}-27t+5
integral from 0 to 1 of 5/(sqrt(4-x^2))
\int\:_{0}^{1}\frac{5}{\sqrt{4-x^{2}}}dx
tangent of y=ln(x^4-4095),(8,0)
tangent\:y=\ln(x^{4}-4095),(8,0)
integral of-sec(x)tan(x)
\int\:-\sec(x)\tan(x)dx
derivative of ln(x+sqrt(x^2-9))
\frac{d}{dx}(\ln(x+\sqrt{x^{2}-9}))
derivative of (x+1/(x^3+x-2))
\frac{d}{dx}(\frac{x+1}{x^{3}+x-2})
derivative of xln(5x)
\frac{d}{dx}(x\ln(5x))
tangent of 3x^2-4x+6,\at x=2
tangent\:3x^{2}-4x+6,\at\:x=2
y^{''}+4y=0,y(0)=1,y(1)=0
y^{\prime\:\prime\:}+4y=0,y(0)=1,y(1)=0
d/(dt)(ae^tcos(2t)+be^tsin(2t))
\frac{d}{dt}(ae^{t}\cos(2t)+be^{t}\sin(2t))
limit as x approaches 0 of (1+x)^2-1
\lim\:_{x\to\:0}((1+x)^{2}-1)
limit as x approaches 1 of sqrt(6x^2+1)
\lim\:_{x\to\:1}(\sqrt{6x^{2}+1})
limit as x approaches 1 of \sqrt[3]{x}-1
\lim\:_{x\to\:1}(\sqrt[3]{x}-1)
integral of 1/(4+v^2)
\int\:\frac{1}{4+v^{2}}dv
domain of f(x)=(sqrt(1-x^2))/x
domain\:f(x)=\frac{\sqrt{1-x^{2}}}{x}
derivative of y=10csc(5x^5-4x+4)
derivative\:y=10\csc(5x^{5}-4x+4)
integral of (3x^2)/((1-x)(x^2+x+1))
\int\:\frac{3x^{2}}{(1-x)(x^{2}+x+1)}dx
limit as x approaches 4 of-x^2+6x-3
\lim\:_{x\to\:4}(-x^{2}+6x-3)
sum from n=0 to infinity of x^{2n+1}
\sum\:_{n=0}^{\infty\:}x^{2n+1}
derivative of 1/(sqrt(1-2x))
\frac{d}{dx}(\frac{1}{\sqrt{1-2x}})
derivative of y=xsin(x)+2
derivative\:y=x\sin(x)+2
x^{''}-x^'-6x=6e^{3t}+2e^{-2t}
x^{\prime\:\prime\:}-x^{\prime\:}-6x=6e^{3t}+2e^{-2t}
limit as x approaches 0 of (sec(x-1))/(xsec(x))
\lim\:_{x\to\:0}(\frac{\sec(x-1)}{x\sec(x)})
integral of e^{kt}
\int\:e^{kt}dt
(\partial)/(\partial x)((5x^3y+4y^5)^3)
\frac{\partial\:}{\partial\:x}((5x^{3}y+4y^{5})^{3})
(dy)/(dx)+4y-e^{-x}=0,y(0)= 4/3
\frac{dy}{dx}+4y-e^{-x}=0,y(0)=\frac{4}{3}
laplacetransform sin^2(6t)
laplacetransform\:\sin^{2}(6t)
derivative of e^{1/x}-(e^{1/x}/x)
\frac{d}{dx}(e^{\frac{1}{x}}-\frac{e^{\frac{1}{x}}}{x})
derivative of sqrt(x^3+x^5)
\frac{d}{dx}(\sqrt{x^{3}+x^{5}})
derivative of-5cot(x+3sec(x))
\frac{d}{dx}(-5\cot(x)+3\sec(x))
integral of x/(sqrt(2-x^2))
\int\:\frac{x}{\sqrt{2-x^{2}}}dx
limit as x approaches infinity of 7x-3
\lim\:_{x\to\:\infty\:}(7x-3)
(\partial)/(\partial x)((x^2)/(x^2+1))
\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{x^{2}+1})
((f(t))/(g(t)))'
(\frac{f(t)}{g(t)})\prime\:
derivative of sqrt(x)e^{x^2}(x^2+1^{10})
\frac{d}{dx}(\sqrt{x}e^{x^{2}}(x^{2}+1)^{10})
x(dy)/(dx)=2x^2+y,y(1)=3
x\frac{dy}{dx}=2x^{2}+y,y(1)=3
sum from n=2 to infinity of 1/(n^2+5n+6)
\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}+5n+6}
sum from n=1 to infinity of (5n)/(3n-1)
\sum\:_{n=1}^{\infty\:}\frac{5n}{3n-1}
derivative of-(2x/(x-1))
\frac{d}{dx}(-\frac{2x}{x-1})
derivative of f(x)=7(2-3x)^4
derivative\:f(x)=7(2-3x)^{4}
integral of ((x^{am}-x^n))/(sqrt(x))
\int\:\frac{(x^{am}-x^{n})}{\sqrt{x}}dx
y^'+3y=2xe^{-3x}
y^{\prime\:}+3y=2xe^{-3x}
integral of 11^x
\int\:11^{x}dx
limit as x approaches 0-of (x^2)/5-7/x
\lim\:_{x\to\:0-}(\frac{x^{2}}{5}-\frac{7}{x})
d/(dt)(1/(12sqrt(t)))
\frac{d}{dt}(\frac{1}{12\sqrt{t}})
integral of (3xsqrt(2x^2+9))/5
\int\:\frac{3x\sqrt{2x^{2}+9}}{5}dx
integral from 0 to 7 of sqrt(y+9)
\int\:_{0}^{7}\sqrt{y+9}dy
tangent of f(x)=2sin(x),\at x= pi/6
tangent\:f(x)=2\sin(x),\at\:x=\frac{π}{6}
area y=sqrt(x),y= 1/2 x,x=9
area\:y=\sqrt{x},y=\frac{1}{2}x,x=9
integral of cos^3(x/(14))
\int\:\cos^{3}(\frac{x}{14})dx
(\partial)/(\partial x)(e^{5xyz-6})
\frac{\partial\:}{\partial\:x}(e^{5xyz-6})
integral of 1+3x^2y^2
\int\:1+3x^{2}y^{2}dy
derivative of-12
\frac{d}{dx}(-12)
(d^2)/(dx^2)((4x+3)(2x^2+7x-1))
\frac{d^{2}}{dx^{2}}((4x+3)(2x^{2}+7x-1))
taylor e^{(-x^2)/2}
taylor\:e^{\frac{-x^{2}}{2}}
integral of cosh(5x+ln(6))
\int\:\cosh(5x+\ln(6))dx
integral of (3cos(1/2 x))
\int\:(3\cos(\frac{1}{2}x))dx
slope of (-3)(0.15)
slope\:(-3)(0.15)
integral of 3((cos(x)+sin(x))/(sin(2x)))
\int\:3(\frac{\cos(x)+\sin(x)}{\sin(2x)})dx
integral from 2 to 6 of 4+2x^2
\int\:_{2}^{6}4+2x^{2}dx
integral of (10+x)^{-2}
\int\:(10+x)^{-2}dx
integral of (2x^4-x)/(x^3)
\int\:\frac{2x^{4}-x}{x^{3}}dx
integral of (x+7)^7(x+8)
\int\:(x+7)^{7}(x+8)dx
derivative of f(x)=(3x^2-x+1)/x
derivative\:f(x)=\frac{3x^{2}-x+1}{x}
derivative of 4^{ln(x})
\frac{d}{dx}(4^{\ln(x)})
integral from 0 to 1 of 2pix(15-15x)
\int\:_{0}^{1}2πx(15-15x)dx
integral of (x^4-\sqrt[3]{x})/(6sqrt(x))
\int\:\frac{x^{4}-\sqrt[3]{x}}{6\sqrt{x}}dx
integral of 1/x ln(x)
\int\:\frac{1}{x}\ln(x)dx
integral of-(t-6)^2
\int\:-(t-6)^{2}dt
d/(dy)(x^{0.5}y^{0.5})
\frac{d}{dy}(x^{0.5}y^{0.5})
derivative of x^{7/9}
derivative\:x^{\frac{7}{9}}
tangent of f(x)=x^2-7,\at x=2
tangent\:f(x)=x^{2}-7,\at\:x=2
(dx)/(dt)=0.9x(1900-x)
\frac{dx}{dt}=0.9x(1900-x)
limit as x approaches 2-of (x^2)/(x^2+4)
\lim\:_{x\to\:2-}(\frac{x^{2}}{x^{2}+4})
(dy)/(dx)+y/x =9x^5y^2
\frac{dy}{dx}+\frac{y}{x}=9x^{5}y^{2}
d/(dθ)(1+2sin(θ))
\frac{d}{dθ}(1+2\sin(θ))
derivative of sin(6x^2)
\frac{d}{dx}(\sin(6x^{2}))
integral of-(e^{-2x}*(5+2x-2y^2))
\int\:-(e^{-2x}\cdot\:(5+2x-2y^{2}))dx
4xy^'-4y=7x^4
4xy^{\prime\:}-4y=7x^{4}
integral of tan^6(x)sec^2(x)
\int\:\tan^{6}(x)\sec^{2}(x)dx
derivative of x^4+6x
derivative\:x^{4}+6x
domain of f(x)=e^xsin(x)
domain\:f(x)=e^{x}\sin(x)
derivative of x^2sqrt(x^2+1)
\frac{d}{dx}(x^{2}\sqrt{x^{2}+1})
limit as x approaches 0-of |(5x)/x |
\lim\:_{x\to\:0-}(\left|\frac{5x}{x}\right|)
integral of ysin(y)
\int\:y\sin(y)dy
integral of 1/((x^2-4x)^{3/2)}
\int\:\frac{1}{(x^{2}-4x)^{\frac{3}{2}}}dx
integral of (4x^2)/(sqrt(25-x^2))
\int\:\frac{4x^{2}}{\sqrt{25-x^{2}}}dx
integral of ((sin(31x))/(1+cos^2(31x)))
\int\:(\frac{\sin(31x)}{1+\cos^{2}(31x)})dx
integral of 6x^5(x^3-3)^6
\int\:6x^{5}(x^{3}-3)^{6}dx
derivative of e^{t+7}
derivative\:e^{t+7}
limit as x approaches-7+of (-6x)/(x+7)
\lim\:_{x\to\:-7+}(\frac{-6x}{x+7})
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