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Popular Calculus Problems

derivative of (2-x^2)^{1/2}	derivative\:(2-x^{2})^{\frac{1}{2}}
integral from 0 to 1 of 1/(sqrt(x+1))	\int\:_{0}^{1}\frac{1}{\sqrt{x+1}}dx
integral from 0 to 1 of (x+sqrt(x))	\int\:_{0}^{1}(x+\sqrt{x})dx
integral of ((6-x))/(sqrt(4x^2-12x+7))	\int\:\frac{(6-x)}{\sqrt{4x^{2}-12x+7}}dx
integral of (ln(2x))/(2x^2)	\int\:\frac{\ln(2x)}{2x^{2}}dx
integral of t(arctan(t))	\int\:t(\arctan(t))dt
d/(dp)(3p(1-0.5p))	\frac{d}{dp}(3p(1-0.5p))
derivative of (-6/((x+1)^4))	\frac{d}{dx}(\frac{-6}{(x+1)^{4}})
(\partial)/(\partial x)(1+c/x-b/(x^3))	\frac{\partial\:}{\partial\:x}(1+\frac{c}{x}-\frac{b}{x^{3}})
sum from k=1 to infinity of ln(1+1/k)	\sum\:_{k=1}^{\infty\:}\ln(1+\frac{1}{k})
x^2y^'-xy=x^{-7}y^{1/2}	x^{2}y^{\prime\:}-xy=x^{-7}y^{\frac{1}{2}}
limit as x approaches 2 of arctan(((2x^2-8))/(3x^2-6x))	\lim\:_{x\to\:2}(\arctan(\frac{(2x^{2}-8)}{3x^{2}-6x}))
area y=-x^2-2x,y=-2x-4,x=-3,x=0	area\:y=-x^{2}-2x,y=-2x-4,x=-3,x=0
y^{'''}+y^'=tan(x)	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=\tan(x)
derivative of 6sec(x-5x)	\frac{d}{dx}(6\sec(x)-5x)
limit as x approaches-1 of (x+3x^3)^4	\lim\:_{x\to\:-1}((x+3x^{3})^{4})
y^'=e^{x+y}	y^{\prime\:}=e^{x+y}
y^{''}+2y^'-3y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=0,y(0)=1,y^{\prime\:}(0)=1
derivative of y=xe^{3x}	derivative\:y=xe^{3x}
integral of sqrt(1+t^3)	\int\:\sqrt{1+t^{3}}dt
sum from n=0 to infinity of (-1)^n(-2)^n	\sum\:_{n=0}^{\infty\:}(-1)^{n}(-2)^{n}
inverse oflaplace (2s+1)/((s+1)^2)	inverselaplace\:\frac{2s+1}{(s+1)^{2}}
limit as x approaches-2 of 2x^2-8x-3	\lim\:_{x\to\:-2}(2x^{2}-8x-3)
integral of (9x^2-8x+16)/(x^3+4x)	\int\:\frac{9x^{2}-8x+16}{x^{3}+4x}dx
integral of e^{cos(11t)}sin(11t)	\int\:e^{\cos(11t)}\sin(11t)dt
derivative of 1/9	\frac{d}{dx}(\frac{1}{9})
integral of (a+bx^4)/(sqrt(5ax+bx^5))	\int\:\frac{a+bx^{4}}{\sqrt{5ax+bx^{5}}}dx
derivative of ln(21x)	\frac{d}{dx}(\ln(21x))
derivative of g(x)=(x^2+3)(x^2-4x)	derivative\:g(x)=(x^{2}+3)(x^{2}-4x)
laplacetransform-t/4-3/8 sin(2t)	laplacetransform\:-\frac{t}{4}-\frac{3}{8}\sin(2t)
integral from 0 to 1 of pi(x-x^4)	\int\:_{0}^{1}π(x-x^{4})dx
integral of-3x^{-1}	\int\:-3x^{-1}dx
derivative of f(x)=(x^3-2)	derivative\:f(x)=(x^{3}-2)
expand (2x-7)^5	expand\:(2x-7)^{5}
integral of sin(5x)cos(6x)	\int\:\sin(5x)\cos(6x)dx
integral from 3 to 4 of y^3+1/(4y^3)	\int\:_{3}^{4}y^{3}+\frac{1}{4y^{3}}dy
integral of (9x^8+6)/(x^9+6x)	\int\:\frac{9x^{8}+6}{x^{9}+6x}dx
f(x)=sin(7ln(x))	f(x)=\sin(7\ln(x))
derivative of cos(3cos(2sqrt(x)))	\frac{d}{dx}(\cos(3\cos(2\sqrt{x})))
laplacetransform e^{-2s}	laplacetransform\:e^{-2s}
f^'(x)=-1/x (f(x))	f^{\prime\:}(x)=-\frac{1}{x}(f(x))
inverse oflaplace (s+1)/(s^2+2s+2)	inverselaplace\:\frac{s+1}{s^{2}+2s+2}
integral of 1/x-1	\int\:\frac{1}{x}-1dx
integral of (1-cos^2(x))sin(x)	\int\:(1-\cos^{2}(x))\sin(x)dx
integral of 11sec^{-2}(xta)n^3x	\int\:11\sec^{-2}(xta)n^{3}xdx
(\partial)/(\partial x)(ye^x+xe^{-y})	\frac{\partial\:}{\partial\:x}(ye^{x}+xe^{-y})
taylor 1/((7+x)^2)	taylor\:\frac{1}{(7+x)^{2}}
tangent of y=(4x)/(x^2+1),(1,2)	tangent\:y=\frac{4x}{x^{2}+1},(1,2)
derivative of \sqrt[5]{x^2}-x^pi	derivative\:\sqrt[5]{x^{2}}-x^{π}
integral of 2+t	\int\:2+tdt
derivative of f(x)=\sqrt[4]{t}	derivative\:f(x)=\sqrt[4]{t}
limit as x approaches infinity of x^{-2}e^{2x}	\lim\:_{x\to\:\infty\:}(x^{-2}e^{2x})
derivative of e^{(2x^3-2})	\frac{d}{dx}(e^{(2x)^{3}-2})
y^'=((4t^3+1))/(2y-6)	y^{\prime\:}=\frac{(4t^{3}+1)}{2y-6}
integral of tan^3(x)sec^2(x)	\int\:\tan^{3}(x)\sec^{2}(x)dx
area y=15-x^2,y=x^2-3	area\:y=15-x^{2},y=x^{2}-3
integral from 1 to 5 of 1/(1+2x)	\int\:_{1}^{5}\frac{1}{1+2x}dx
(\partial)/(\partial x)((x^2y)/(x^4+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}y}{x^{4}+y^{2}})
area \|x-2\|,0=x-3y+6	area\:\left\|x-2\right\|,0=x-3y+6
integral from 2 to 3 of (40)/(sqrt(3-x))	\int\:_{2}^{3}\frac{40}{\sqrt{3-x}}dx
derivative of (cos(x)/(1+asin(x)))	\frac{d}{dx}(\frac{\cos(x)}{1+a\sin(x)})
integral of 6/(1+x^2)	\int\:\frac{6}{1+x^{2}}dx
limit as x approaches 1 of f(x)+g(x)	\lim\:_{x\to\:1}(f(x)+g(x))
sum from n=2 to infinity of n/(2n^2-3)	\sum\:_{n=2}^{\infty\:}\frac{n}{2n^{2}-3}
(\partial)/(\partial x)(e^{-xy}+y^3x^4)	\frac{\partial\:}{\partial\:x}(e^{-xy}+y^{3}x^{4})
derivative of 3x^3+2x^2-1x+5	\frac{d}{dx}(3x^{3}+2x^{2}-1x+5)
integral from 0 to 3 of e^{-x^2}	\int\:_{0}^{3}e^{-x^{2}}dx
limit as x approaches pi of ln(cos(x)-3)	\lim\:_{x\to\:π}(\ln(\cos(x)-3))
integral of y^2z+2xz^2	\int\:y^{2}z+2xz^{2}dx
derivative of 2/x	derivative\:\frac{2}{x}
integral of (-4sin(2t))	\int\:(-4\sin(2t))dt
limit as x approaches 0-of (x^2)/7-6/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{7}-\frac{6}{x})
integral from-3 to 3 of (3-\|x\|)	\int\:_{-3}^{3}(3-\left\|x\right\|)dx
(dy}{dx}-\frac{2y)/x =x^2	\frac{dy}{dx}-\frac{2y}{x}=x^{2}
slope ofintercept (2.3)(5.2)	slopeintercept\:(2.3)(5.2)
f^'(x)=x\|x\|	f^{\prime\:}(x)=x\left\|x\right\|
integral of 2\sqrt[5]{x^4}-7x^3+10e^x-1	\int\:2\sqrt[5]{x^{4}}-7x^{3}+10e^{x}-1dx
derivative of x^{x^3-2x}	derivative\:x^{x^{3}-2x}
integral of x^2(3-2x^3)^{1/3}	\int\:x^{2}(3-2x^{3})^{\frac{1}{3}}dx
(\partial)/(\partial x)((x+y^2)e^{x-y})	\frac{\partial\:}{\partial\:x}((x+y^{2})e^{x-y})
integral from-6 to 1 of-2x^2-10x+12	\int\:_{-6}^{1}-2x^{2}-10x+12dx
integral of ((x-1)^2-(x+1)^2)(x^3+1)	\int\:((x-1)^{2}-(x+1)^{2})(x^{3}+1)dx
(\partial)/(\partial x)(zln(y)+e^2)	\frac{\partial\:}{\partial\:x}(z\ln(y)+e^{2})
derivative of \sqrt[3]{9x^2+4}	\frac{d}{dx}(\sqrt[3]{9x^{2}+4})
derivative of x^2arcsinh(9x)	\frac{d}{dx}(x^{2}\arcsinh(9x))
integral of 1/(x^5)-3/(x^2)	\int\:\frac{1}{x^{5}}-\frac{3}{x^{2}}dx
xy^'+2y=x^2-x+1	xy^{\prime\:}+2y=x^{2}-x+1
tangent of f(x)=ln(x^2-9x+1),(9,0)	tangent\:f(x)=\ln(x^{2}-9x+1),(9,0)
slope of (-2,2),(1,-2)	slope\:(-2,2),(1,-2)
laplacetransform 6t^2	laplacetransform\:6t^{2}
integral of 1/(sqrt(484-x^2))	\int\:\frac{1}{\sqrt{484-x^{2}}}dx
derivative of In^2x	\frac{d}{dx}(In^{2}x)
sum from n=1 to infinity}(e^{2n of)/n	\sum\:_{n=1}^{\infty\:}\frac{e^{2n}}{n}
integral from 1 to e of (ln(x))/(x^2)	\int\:_{1}^{e}\frac{\ln(x)}{x^{2}}dx
derivative of f(x)=x^8	derivative\:f(x)=x^{8}
derivative of e^{-x}+x^3-6	\frac{d}{dx}(e^{-x}+x^{3}-6)
integral of 2*x	\int\:2\cdot\:xdx
limit as x approaches 0 of (sin(4x))/4	\lim\:_{x\to\:0}(\frac{\sin(4x)}{4})
tangent of y= 2/(x-2)	tangent\:y=\frac{2}{x-2}
integral of (1-2x)/(e^{-2x)}	\int\:\frac{1-2x}{e^{-2x}}dx

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