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Popular Calculus Problems
y^{''}+6y^'+13y=0
y^{\prime\:\prime\:}+6y^{\prime\:}+13y=0
integral of (x^3)/(64)
\int\:\frac{x^{3}}{64}dx
integral of (x^2-sqrt(x)+3)
\int\:(x^{2}-\sqrt{x}+3)dx
integral of (2x)/(x^2+y^4)
\int\:\frac{2x}{x^{2}+y^{4}}dx
tangent of f(x)= 1/(sqrt(2x))x^9
tangent\:f(x)=\frac{1}{\sqrt{2x}}x^{9}
slope ofintercept (-1,7),(3,-1)
slopeintercept\:(-1,7),(3,-1)
limit as x approaches 0 of (arccos(1-x))/(sqrt(x))
\lim\:_{x\to\:0}(\frac{\arccos(1-x)}{\sqrt{x}})
integral of 1-2x^2+x^4
\int\:1-2x^{2}+x^{4}dx
tangent of x^2+y^2=169,(-12,5)
tangent\:x^{2}+y^{2}=169,(-12,5)
sum from n=6 to infinity of (7^n)/(12^n)
\sum\:_{n=6}^{\infty\:}\frac{7^{n}}{12^{n}}
integral of 6cos(sqrt(5x))
\int\:6\cos(\sqrt{5x})dx
integral from 0 to 3 of 4pi((x^3)/3)
\int\:_{0}^{3}4π(\frac{x^{3}}{3})dx
derivative of 1+10sqrt(t)
derivative\:1+10\sqrt{t}
integral of 10-x
\int\:10-xdx
tangent of f(x)=(x^3)/4 ,(-6,-54)
tangent\:f(x)=\frac{x^{3}}{4},(-6,-54)
integral of (sqrt(x)+6)/(\sqrt[3]{x)}
\int\:\frac{\sqrt{x}+6}{\sqrt[3]{x}}dx
(\partial)/(\partial x)(sin(3x)cos(2y))
\frac{\partial\:}{\partial\:x}(\sin(3x)\cos(2y))
integral of (sin(x))^{1/3}cos(x)
\int\:(\sin(x))^{\frac{1}{3}}\cos(x)dx
integral from 6 to 13 of ln(x-6)
\int\:_{6}^{13}\ln(x-6)dx
limit as x approaches 0 of 25
\lim\:_{x\to\:0}(25)
derivative of arctan(10x)
\frac{d}{dx}(\arctan(10x))
derivative of ln(sqrt(x^2-9))
\frac{d}{dx}(\ln(\sqrt{x^{2}-9}))
derivative of sqrt(x^2+(1/2 x-5)^2)
derivative\:\sqrt{x^{2}+(\frac{1}{2}x-5)^{2}}
integral of x/(\sqrt[3]{x+12)}
\int\:\frac{x}{\sqrt[3]{x+12}}dx
derivative of f(x)=6sqrt(x)sin(x)
derivative\:f(x)=6\sqrt{x}\sin(x)
(dy)/(dx)=xsqrt(x-9)
\frac{dy}{dx}=x\sqrt{x-9}
area y=sqrt(3-x),y=-sqrt(3-x),y=x-1
area\:y=\sqrt{3-x},y=-\sqrt{3-x},y=x-1
limit as x approaches 1 of 4x^2-7x+5
\lim\:_{x\to\:1}(4x^{2}-7x+5)
integral of e^xcos(5x)
\int\:e^{x}\cos(5x)dx
-60=(d^2y)/(dx^2)
-60=\frac{d^{2}y}{dx^{2}}
derivative of f(x)=4e^{0.5x}
derivative\:f(x)=4e^{0.5x}
(\partial)/(\partial x)(x^5+x^2y+x+5)
\frac{\partial\:}{\partial\:x}(x^{5}+x^{2}y+x+5)
y^{''}-4y^'+3y=0,y(0)=1,y^'(0)=3
y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0,y(0)=1,y^{\prime\:}(0)=3
limit as x approaches 1 of e^{x^2-4x+1}
\lim\:_{x\to\:1}(e^{x^{2}-4x+1})
integral of sin(inx)
\int\:\sin(inx)dx
integral from-1 to 0 of 1
\int\:_{-1}^{0}1
integral of e^{x/y}
\int\:e^{\frac{x}{y}}dx
limit as x approaches 0-of 8/x-8/(|x|)
\lim\:_{x\to\:0-}(\frac{8}{x}-\frac{8}{\left|x\right|})
integral of (sqrt(x)-2x^2)/x
\int\:\frac{\sqrt{x}-2x^{2}}{x}dx
integral of arccos(y)
\int\:\arccos(y)dy
integral from-2 to 3 of 2x^2+5
\int\:_{-2}^{3}2x^{2}+5dx
limit as x approaches-7 of 1/(x+7)
\lim\:_{x\to\:-7}(\frac{1}{x+7})
derivative of cot^3(pi-x)
\frac{d}{dx}(\cot^{3}(π-x))
limit as x approaches-3 of 1/(x-1)
\lim\:_{x\to\:-3}(\frac{1}{x-1})
slope of (-2,3),(2,-2)
slope\:(-2,3),(2,-2)
limit as x approaches 1-of 9/(x^3-1)
\lim\:_{x\to\:1-}(\frac{9}{x^{3}-1})
y^'=((x^2+y^2))/(2xy)
y^{\prime\:}=\frac{(x^{2}+y^{2})}{2xy}
(\partial)/(\partial y)(1/(x+y^2))
\frac{\partial\:}{\partial\:y}(\frac{1}{x+y^{2}})
integral of (x-3)/(sqrt(6x-x^2))
\int\:\frac{x-3}{\sqrt{6x-x^{2}}}dx
integral of 7\sqrt[6]{x^5}
\int\:7\sqrt[6]{x^{5}}dx
derivative of ln(cos(sqrt(x)))
\frac{d}{dx}(\ln(\cos(\sqrt{x})))
integral of (tan^2(x))/(sec^5(x))
\int\:\frac{\tan^{2}(x)}{\sec^{5}(x)}dx
integral of w/(sqrt(16-w^2))
\int\:\frac{w}{\sqrt{16-w^{2}}}dw
derivative of x/(sqrt(x^2+7))
\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+7}})
limit as x approaches 0 of 7cot^4(3x)
\lim\:_{x\to\:0}(7\cot^{4}(3x))
integral of (cos(sqrt(x)))/x
\int\:\frac{\cos(\sqrt{x})}{x}dx
derivative of f(x)=5(7+sqrt(x))
derivative\:f(x)=5(7+\sqrt{x})
derivative of 1/((1+x^2))
\frac{d}{dx}(\frac{1}{(1+x^{2})})
limit as x approaches 1-of x
\lim\:_{x\to\:1-}(x)
integral of 2x^9e^{-x^5}
\int\:2x^{9}e^{-x^{5}}dx
integral of 9/(x^2sqrt(x^2+4))
\int\:\frac{9}{x^{2}\sqrt{x^{2}+4}}dx
(\partial)/(\partial x)(x^2+zsin(xyz))
\frac{\partial\:}{\partial\:x}(x^{2}+z\sin(xyz))
integral of ((1-u^2-u-u^3))/(1+u^2)
\int\:\frac{(1-u^{2}-u-u^{3})}{1+u^{2}}du
derivative of sqrt(x^2-3)
derivative\:\sqrt{x^{2}-3}
d/(dz)(ln(sqrt((b^2-z^2)/(b^2+z^2))))
\frac{d}{dz}(\ln(\sqrt{\frac{b^{2}-z^{2}}{b^{2}+z^{2}}}))
y^{''}+9y=4csc^2(3t)
y^{\prime\:\prime\:}+9y=4\csc^{2}(3t)
limit as x approaches 0 of (2x)/(tan(x))
\lim\:_{x\to\:0}(\frac{2x}{\tan(x)})
integral from 10 to 20 of sqrt(400-x^2)
\int\:_{10}^{20}\sqrt{400-x^{2}}dx
integral of sqrt(6-4x-4x^2)
\int\:\sqrt{6-4x-4x^{2}}dx
derivative of x^6(1-x^4)
\frac{d}{dx}(x^{6}(1-x)^{4})
derivative of (dy/(dx))=1
\frac{d}{dx}(\frac{dy}{dx})=1
integral of ((3x-2)^2-(3x+2)^2)/(x^2)
\int\:\frac{(3x-2)^{2}-(3x+2)^{2}}{x^{2}}dx
(dy)/(dx)=sin(x)y+e^x
\frac{dy}{dx}=\sin(x)y+e^{x}
derivative of y=x^{1-x}
derivative\:y=x^{1-x}
tangent of f(x)= 1/((1+x^2))
tangent\:f(x)=\frac{1}{(1+x^{2})}
derivative of 4-(20/(x^3)+3/(x^5))
\frac{d}{dx}(4-\frac{20}{x^{3}}+\frac{3}{x^{5}})
tangent of f(x)=x^2+x,\at (x=1)
tangent\:f(x)=x^{2}+x,\at\:(x=1)
(\partial)/(\partial x)(y^2+x^2)
\frac{\partial\:}{\partial\:x}(y^{2}+x^{2})
3xy^2y^'=3x^4+y^3
3xy^{2}y^{\prime\:}=3x^{4}+y^{3}
slope ofintercept (3.7)(6.12)
slopeintercept\:(3.7)(6.12)
d/(dy)(csc(y))
\frac{d}{dy}(\csc(y))
integral of (cos(x))/(sin^{19)(x)}
\int\:\frac{\cos(x)}{\sin^{19}(x)}dx
integral from 0 to 1 of 4ln(3x)
\int\:_{0}^{1}4\ln(3x)dx
integral of 1/(sqrt(x^2+2x+37))
\int\:\frac{1}{\sqrt{x^{2}+2x+37}}dx
integral of te^{5t}
\int\:te^{5t}dt
limit as x approaches 2 of 1/2 x^2+2
\lim\:_{x\to\:2}(\frac{1}{2}x^{2}+2)
integral of (9x^2-5x+3)
\int\:(9x^{2}-5x+3)dx
limit as x approaches 2 of (x-2)^{x-2}
\lim\:_{x\to\:2}((x-2)^{x-2})
derivative of (1/(2x+3)^3)
\frac{d}{dx}((\frac{1}{2x+3})^{3})
derivative of f(x)=arctan((1+x)/(1-x))
derivative\:f(x)=\arctan(\frac{1+x}{1-x})
(\partial)/(\partial x)(1+x^3+y^4)
\frac{\partial\:}{\partial\:x}(1+x^{3}+y^{4})
integral of (3x+4)/(x+3)
\int\:\frac{3x+4}{x+3}dx
integral from 0 to 1 of-10(x^2+1)e^{-x}
\int\:_{0}^{1}-10(x^{2}+1)e^{-x}dx
(dy}{dx}=\frac{(x^2-y))/x
\frac{dy}{dx}=\frac{(x^{2}-y)}{x}
integral of x+2x\sqrt{x
\int\:x+2x\sqrt{d}xdx
limit as x approaches 0+of x^2-x-ln(x)
\lim\:_{x\to\:0+}(x^{2}-x-\ln(x))
integral of (x^3-2x-2)/(x^4+2x^3+3x^2)
\int\:\frac{x^{3}-2x-2}{x^{4}+2x^{3}+3x^{2}}dx
derivative of x^{4/5}(x-6^2)
\frac{d}{dx}(x^{\frac{4}{5}}(x-6)^{2})
derivative of 1+cot^2(x)
\frac{d}{dx}(1+\cot^{2}(x))
limit as x approaches 0 of x/(-2x^4-14x)
\lim\:_{x\to\:0}(\frac{x}{-2x^{4}-14x})
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