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Popular Calculus Problems

limit as x approaches 4 of (13x-52)/(2x-8)	\lim\:_{x\to\:4}(\frac{13x-52}{2x-8})
integral of (xcos(x)-sin(x))/(x^2)	\int\:\frac{x\cos(x)-\sin(x)}{x^{2}}dx
limit as x approaches 5 of 3x^2-6x+8	\lim\:_{x\to\:5}(3x^{2}-6x+8)
tangent of 1/(x^2)(1.1)	tangent\:\frac{1}{x^{2}}(1.1)
integral of+4x(x^2-3)^5	\int\:+4x(x^{2}-3)^{5}dx
integral of (4cos(x)+5sin(x))	\int\:(4\cos(x)+5\sin(x))dx
(\partial)/(\partial x)(x^{x^2-y^2})	\frac{\partial\:}{\partial\:x}(x^{x^{2}-y^{2}})
derivative of ((-2x^2+2x)/((3x-3)))	\frac{d}{dx}(\frac{(-2x^{2}+2x)}{(3x-3)})
derivative of (40/(3x^{1/3)})	\frac{d}{dx}(\frac{40}{3x^{\frac{1}{3}}})
limit as x approaches 0 of (sqrt(x+4)-2)/(sin(5x))	\lim\:_{x\to\:0}(\frac{\sqrt{x+4}-2}{\sin(5x)})
integral of 39arctan(sqrt(x))	\int\:39\arctan(\sqrt{x})dx
integral of 6tsin(t)	\int\:6t\sin(t)dt
area y=5x-x^2,x	area\:y=5x-x^{2},x
limit as x approaches 0 of 1/(x^2-x)	\lim\:_{x\to\:0}(\frac{1}{x^{2}-x})
integral of t^8ln(t)	\int\:t^{8}\ln(t)dt
derivative of f(x)= 1/(sqrt(x+6))	derivative\:f(x)=\frac{1}{\sqrt{x+6}}
derivative of (7x^{ln(7x)})	\frac{d}{dx}((7x)^{\ln(7x)})
integral from 0 to 2pi of sin(t)	\int\:_{0}^{2π}\sin(t)dt
derivative of 9log_{2}(x)	\frac{d}{dx}(9\log_{2}(x))
limit as n approaches infinity of e^{-n}	\lim\:_{n\to\:\infty\:}(e^{-n})
(\partial)/(\partial y)(2x+2y)	\frac{\partial\:}{\partial\:y}(2x+2y)
derivative of e^{x/((x-4))}	derivative\:e^{\frac{x}{(x-4)}}
derivative of \sqrt[3]{y}	derivative\:\sqrt[3]{y}
slope of y= 5/(sqrt(x))	slope\:y=\frac{5}{\sqrt{x}}
y^{''}+6y^'+9=0	y^{\prime\:\prime\:}+6y^{\prime\:}+9=0
derivative of e^{-0.5x}(4-x-2)	\frac{d}{dx}(e^{-0.5x}(4-x)-2)
maclaurin (1-x+x^2)e^x	maclaurin\:(1-x+x^{2})e^{x}
(\partial)/(\partial x)(x^5-6x+4y^3-y^2)	\frac{\partial\:}{\partial\:x}(x^{5}-6x+4y^{3}-y^{2})
slope of (4.6)(3.1)	slope\:(4.6)(3.1)
derivative of f(9)=3.6sqrt(x)+500	derivative\:f(9)=3.6\sqrt{x}+500
(\partial)/(\partial x)(ln(y)*ln(x^2+1))	\frac{\partial\:}{\partial\:x}(\ln(y)\cdot\:\ln(x^{2}+1))
integral of x(5x+1)^{19}	\int\:x(5x+1)^{19}dx
integral of e^{-bt}	\int\:e^{-bt}dt
integral of 5/(9+5x)	\int\:\frac{5}{9+5x}dx
integral from 0 to a of x^2e^x	\int\:_{0}^{a}x^{2}e^{x}dx
(\partial)/(\partial x)(6x^3y^2)	\frac{\partial\:}{\partial\:x}(6x^{3}y^{2})
limit as x approaches 1 of (5x-1)^{-2}	\lim\:_{x\to\:1}((5x-1)^{-2})
derivative of (4x-4(3x^3-x^2+1))	\frac{d}{dx}((4x-4)(3x^{3}-x^{2}+1))
area y= 1/(16x^2),y=x,y= x/(18)	area\:y=\frac{1}{16x^{2}},y=x,y=\frac{x}{18}
derivative of f(x)=sin(cos(4x))	derivative\:f(x)=\sin(\cos(4x))
integral of 4xcos(4x)	\int\:4x\cos(4x)dx
integral of (2^x-x^2)^2	\int\:(2^{x}-x^{2})^{2}dx
derivative of f(x)=1.5e^{0.76x}	derivative\:f(x)=1.5e^{0.76x}
laplacetransform 4e^{(3t)}	laplacetransform\:4e^{(3t)}
(\partial)/(\partial x)(x^3e^{xy}+2y)	\frac{\partial\:}{\partial\:x}(x^{3}e^{xy}+2y)
integral of 20xe^{0.1x^2}	\int\:20xe^{0.1x^{2}}dx
integral of (2x)/(4x^2+3)	\int\:\frac{2x}{4x^{2}+3}dx
derivative of (25/(x^3))	\frac{d}{dx}(\frac{25}{x^{3}})
integral of sin^x(x	\int\:\sin^{x}(d)xdx
integral of t/(sqrt(1-t^2))	\int\:\frac{t}{\sqrt{1-t^{2}}}dt
sin(x)dx+ydy=0,y(0)=-2	\sin(x)dx+ydy=0,y(0)=-2
integral of 1/((x^2+10x+24))	\int\:\frac{1}{(x^{2}+10x+24)}dx
derivative of ln(arctan(x))	\frac{d}{dx}(\ln(\arctan(x)))
(dy)/(dx)-3y=0	\frac{dy}{dx}-3y=0
sum from n=1 to infinity of (-0.7)^{n-1}	\sum\:_{n=1}^{\infty\:}(-0.7)^{n-1}
(\partial)/(\partial t)(x/t)	\frac{\partial\:}{\partial\:t}(\frac{x}{t})
integral from 0 to 3 of pi(9x^2-x^4)	\int\:_{0}^{3}π(9x^{2}-x^{4})dx
limit as x approaches 1 of e^{6x^5-6x}	\lim\:_{x\to\:1}(e^{6x^{5}-6x})
integral of-(17)/(x^{18)}	\int\:-\frac{17}{x^{18}}dx
derivative of y=f(u)=u(y,x)^3-4yu(y,x)=g(x)=x^3+3	derivative\:y=f(u)=u(y,x)^{3}-4yu(y,x)=g(x)=x^{3}+3
tangent of f(x)=x^2-2,\at x=-5,23	tangent\:f(x)=x^{2}-2,\at\:x=-5,23
limit as x approaches 3pi of e^{sin(x)}	\lim\:_{x\to\:3π}(e^{\sin(x)})
derivative of f(x)=\sqrt[3]{x-8}	derivative\:f(x)=\sqrt[3]{x-8}
limit as x approaches 3 of (\|x-3\|)/(3-x)	\lim\:_{x\to\:3}(\frac{\left\|x-3\right\|}{3-x})
integral of (1-2x)e^{-2x}	\int\:(1-2x)e^{-2x}dx
derivative of 3/y	derivative\:\frac{3}{y}
integral of x/(\sqrt[4]{5-2x^2)}	\int\:\frac{x}{\sqrt[4]{5-2x^{2}}}dx
derivative of e^p	derivative\:e^{p}
inverse oflaplace 3/(5(s-3)^2+80)	inverselaplace\:\frac{3}{5(s-3)^{2}+80}
area x^2+2x+1,2x+5,-2,2	area\:x^{2}+2x+1,2x+5,-2,2
integral of x^2+4x+5	\int\:x^{2}+4x+5dx
ydy=4xsqrt(y^2+1)dx	ydy=4x\sqrt{y^{2}+1}dx
(dy)/(dx)=(x^2+y^2)/(x^2)	\frac{dy}{dx}=\frac{x^{2}+y^{2}}{x^{2}}
(x/(x^2+y^4))dx+(((2y^3))/(x^2+y^4))dy=0	(\frac{x}{x^{2}+y^{4}})dx+(\frac{(2y^{3})}{x^{2}+y^{4}})dy=0
derivative of (7x^3+x/(6sqrt(x)))	\frac{d}{dx}(\frac{7x^{3}+x}{6\sqrt{x}})
derivative of log_{10}(1/x)	\frac{d}{dx}(\log_{10}(\frac{1}{x}))
integral of 1/(y(y^3-1))	\int\:\frac{1}{y(y^{3}-1)}dy
y^{''}-6y^'=4x	y^{\prime\:\prime\:}-6y^{\prime\:}=4x
integral of (24)/((399x-1)(399+1))	\int\:\frac{24}{(399x-1)(399+1)}dx
derivative of arcsin(u)	derivative\:\arcsin(u)
derivative of 3x^2+2xy-y^2	\frac{d}{dx}(3x^{2}+2xy-y^{2})
derivative of f(x)=(3-x)^4(x+5)^3	derivative\:f(x)=(3-x)^{4}(x+5)^{3}
(dy)/(dt)=y*ln(y)	\frac{dy}{dt}=y\cdot\:\ln(y)
(\partial)/(\partial x)(7xe^{x^2+y^2})	\frac{\partial\:}{\partial\:x}(7xe^{x^{2}+y^{2}})
(\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2)	\frac{\partial\:}{\partial\:z}(\frac{x^{2}+z^{2}}{y}+xyz+5xz^{2})
integral of (e^x+1)/(e^x-1)	\int\:\frac{e^{x}+1}{e^{x}-1}dx
derivative of 1/(\sqrt[3]{x})	\frac{d}{dx}(\frac{1}{\sqrt[3]{x}})
(\partial)/(\partial x)(asin(x)sin(y))	\frac{\partial\:}{\partial\:x}(a\sin(x)\sin(y))
(\partial)/(\partial y)(x^2y-y^2)	\frac{\partial\:}{\partial\:y}(x^{2}y-y^{2})
(\partial)/(\partial x)((2s-3t)/(3s+5t))	\frac{\partial\:}{\partial\:x}(\frac{2s-3t}{3s+5t})
integral of 1/((x^2+9)^3)	\int\:\frac{1}{(x^{2}+9)^{3}}dx
derivative of (x^4+5x^2-5)^4	derivative\:(x^{4}+5x^{2}-5)^{4}
(\partial)/(\partial x)(2+xln(xy-9))	\frac{\partial\:}{\partial\:x}(2+x\ln(xy-9))
laplacetransform u^1	laplacetransform\:u^{1}
derivative of f(x)= 3/8 x^4-2-(10)/x	derivative\:f(x)=\frac{3}{8}x^{4}-2-\frac{10}{x}
derivative of f(x)=(3x^2-1)^2	derivative\:f(x)=(3x^{2}-1)^{2}
area 2sqrt(x),y= 1/3 x	area\:2\sqrt{x},y=\frac{1}{3}x
derivative of x^3+3x^2-9x+4	\frac{d}{dx}(x^{3}+3x^{2}-9x+4)
limit as x approaches 2 of sqrt(kx)	\lim\:_{x\to\:2}(\sqrt{kx})
integral of sqrt(9-y^2)	\int\:\sqrt{9-y^{2}}dy

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