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Popular Calculus Problems

integral from 1 to 3 of x^5+1/(4x^5)	\int\:_{1}^{3}x^{5}+\frac{1}{4x^{5}}dx
area y=x,y=0,y= 1/(x^2)	area\:y=x,y=0,y=\frac{1}{x^{2}}
limit as x approaches 0 of (1-3x)^{7/x}	\lim\:_{x\to\:0}((1-3x)^{\frac{7}{x}})
integral of (sqrt(t)-3)/(sqrt(t)+1)	\int\:\frac{\sqrt{t}-3}{\sqrt{t}+1}dt
integral of x*(ln(x))^2	\int\:x\cdot\:(\ln(x))^{2}dx
derivative of (x+1/(x^2-y+1))	\frac{d}{dx}(\frac{x+1}{x^{2}-y+1})
y^{''}-6y^'+9=0	y^{\prime\:\prime\:}-6y^{\prime\:}+9=0
slope of (-5)(0.7)	slope\:(-5)(0.7)
integral of 1/(e^v)	\int\:\frac{1}{e^{v}}dv
(\partial)/(\partial y)((x^2+y^2)/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}+y^{2}}{x+y})
integral of 2x^{2x}(ln(x)+1)	\int\:2x^{2x}(\ln(x)+1)dx
derivative of e^{(-x/y})	\frac{d}{dx}(e^{\frac{-x}{y}})
integral from 2 to 5 of 1/(x+1)	\int\:_{2}^{5}\frac{1}{x+1}dx
(\partial)/(\partial x)(x/(x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+2y^{2}})
integral of (sqrt(81-x^2))/(x^2)	\int\:\frac{\sqrt{81-x^{2}}}{x^{2}}dx
y=3x^4-12x^3	y=3x^{4}-12x^{3}
limit as x approaches-1 of x	\lim\:_{x\to\:-1}(x)
derivative of f(x)=(5x^{3/2}-15^{1/2})/2	derivative\:f(x)=\frac{5x^{\frac{3}{2}}-15^{\frac{1}{2}}}{2}
integral from-5 to 5 of 25-x^2	\int\:_{-5}^{5}25-x^{2}dx
derivative of (1/(x^2-3/(x^4))*(x+5x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{3}{x^{4}})\cdot\:(x+5x^{3}))
derivative of arccos(x/3)	\frac{d}{dx}(\arccos(\frac{x}{3}))
derivative of a(e^{-5x}-5e^{-5x}x)	\frac{d}{dx}(a(e^{-5x}-5e^{-5x}x))
(d^2)/(dx^2)(sqrt(x+1))	\frac{d^{2}}{dx^{2}}(\sqrt{x+1})
derivative of x/(ln(x))	derivative\:\frac{x}{\ln(x)}
derivative of-16t^2+83t+4	derivative\:-16t^{2}+83t+4
derivative of 3(2cos(x-xsin(x)))	\frac{d}{dx}(3(2\cos(x)-x\sin(x)))
integral from 0 to 5 of 12e^{3x}	\int\:_{0}^{5}12e^{3x}dx
(\partial)/(\partial z)(xsin(y)sin(z))	\frac{\partial\:}{\partial\:z}(x\sin(y)\sin(z))
slope of xy-2y^2=4,(9,4)	slope\:xy-2y^{2}=4,(9,4)
derivative of ln(x/(x^2+1))	derivative\:\ln(\frac{x}{x^{2}+1})
inverse oflaplace (3s+1)/(s^2(s^2+4))	inverselaplace\:\frac{3s+1}{s^{2}(s^{2}+4)}
xy^'-y=(x^2)/(y^2)	xy^{\prime\:}-y=\frac{x^{2}}{y^{2}}
(d^2)/(dx^2)(sqrt(2/(4x+3)))	\frac{d^{2}}{dx^{2}}(\sqrt{\frac{2}{4x+3}})
laplacetransform 25	laplacetransform\:25
area 4-x^2,3x	area\:4-x^{2},3x
integral of (3x^2-2x+1)	\int\:(3x^{2}-2x+1)dx
integral of (sqrt(x^2-1))/x	\int\:\frac{\sqrt{x^{2}-1}}{x}dx
f(x)=ln(1+x^2)	f(x)=\ln(1+x^{2})
limit as x approaches 0 of sin((kx)/x)	\lim\:_{x\to\:0}(\sin(\frac{kx}{x}))
integral of x/(2x^2+5x+2)	\int\:\frac{x}{2x^{2}+5x+2}dx
limit as x approaches infinity of-28x^4	\lim\:_{x\to\:\infty\:}(-28x^{4})
implicit (dy)/(dx),xy^2=4	implicit\:\frac{dy}{dx},xy^{2}=4
integral of (2x)/((x+2)(x+1))	\int\:\frac{2x}{(x+2)(x+1)}dx
(\partial)/(\partial x)(4x-2y)	\frac{\partial\:}{\partial\:x}(4x-2y)
tangent of y=4^x,(1,4)	tangent\:y=4^{x},(1,4)
derivative of ((x^2+1)/(x^2-1))^3	derivative\:(\frac{x^{2}+1}{x^{2}-1})^{3}
limit as x approaches 0 of 2x^2	\lim\:_{x\to\:0}(2x^{2})
(dy)/(dy)	\frac{dy}{dy}
d/(d{x)}(({x})/({y)}+({y})/({z)})	\frac{d}{d{x}}(\frac{{x}}{{y}}+\frac{{y}}{{z}})
integral of (x-1)/(sqrt(x)-1)	\int\:\frac{x-1}{\sqrt{x}-1}dx
integral from 1 to 4 of-1sqrt(t)ln(t)	\int\:_{1}^{4}-1\sqrt{t}\ln(t)dt
integral of 8e^{-8x}sin(8x)	\int\:8e^{-8x}\sin(8x)dx
(dy)/(dx)+3/x y=x^5	\frac{dy}{dx}+\frac{3}{x}y=x^{5}
tangent of y= 1/(5+3x),(-1, 1/2)	tangent\:y=\frac{1}{5+3x},(-1,\frac{1}{2})
integral of (2x+3)/(x^2+3x-10)	\int\:\frac{2x+3}{x^{2}+3x-10}dx
integral of (-5x^{-3}+5x^5)	\int\:(-5x^{-3}+5x^{5})dx
limit as x approaches infinity of 1/x+4	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+4)
integral of sin(x)2x	\int\:\sin(x)2xdx
limit as x approaches pi/2+of e^{tan(x)}	\lim\:_{x\to\:\frac{π}{2}+}(e^{\tan(x)})
limit as q approaches 0 of sqrt(9q)+3	\lim\:_{q\to\:0}(\sqrt{9q}+3)
integral of e^{9x}cos(7x)	\int\:e^{9x}\cos(7x)dx
area 9x-x^2,2x,[0,7]	area\:9x-x^{2},2x,[0,7]
(x^2+1)((dy)/(dx))+xy=x	(x^{2}+1)(\frac{dy}{dx})+xy=x
tangent of y= 2/x ,(2,1)	tangent\:y=\frac{2}{x},(2,1)
derivative of (4x+3^2)	\frac{d}{dx}((4x+3)^{2})
integral from 0 to 2 of (2-x)sqrt(x)	\int\:_{0}^{2}(2-x)\sqrt{x}dx
(\partial)/(\partial x)(e^{2xyz-1})	\frac{\partial\:}{\partial\:x}(e^{2xyz-1})
derivative of e^{2x}+4	\frac{d}{dx}(e^{2x}+4)
integral from 0 to 4 of (sqrt(x)+3x)	\int\:_{0}^{4}(\sqrt{x}+3x)dx
integral of e^xsqrt(e^x+5)	\int\:e^{x}\sqrt{e^{x}+5}dx
(dy)/(dx)=(x+y)^2	\frac{dy}{dx}=(x+y)^{2}
tangent of f(x)= 1/(sqrt(2x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{2x}},\at\:x=9
derivative of f(x)=(x^4-5/(x^3))^{-4}	derivative\:f(x)=(x^{4}-\frac{5}{x^{3}})^{-4}
integral from 0 to 3 of x/(x+1)	\int\:_{0}^{3}\frac{x}{x+1}dx
sum from n=1 to infinity of (2n)/(3n-2)	\sum\:_{n=1}^{\infty\:}\frac{2n}{3n-2}
(dy)/(dx)=(y-1)x	\frac{dy}{dx}=(y-1)x
integral of (x^{-3/4})	\int\:(x^{-\frac{3}{4}})dx
(arctan(x))^'	(\arctan(x))^{\prime\:}
(dy)/(dx)= y/x+3x+1	\frac{dy}{dx}=\frac{y}{x}+3x+1
tangent of f(x)= x/(x^2+49)	tangent\:f(x)=\frac{x}{x^{2}+49}
derivative of 2ln\|x-e^x\|	\frac{d}{dx}(2\ln\left\|x-e^{x}\right\|)
(\partial)/(\partial y)(-1/(ln(10)(x-y)))	\frac{\partial\:}{\partial\:y}(-\frac{1}{\ln(10)(x-y)})
f(x)= 8/(sin(x)+cos(x))	f(x)=\frac{8}{\sin(x)+\cos(x)}
area f(x)=x^2-12,g(x)=x-6,[2sqrt(3),6]	area\:f(x)=x^{2}-12,g(x)=x-6,[2\sqrt{3},6]
integral from 0 to 1 of x-sqrt(x)	\int\:_{0}^{1}x-\sqrt{x}dx
tangent of f(x)=1+cos(x),\at x=(3pi)/2	tangent\:f(x)=1+\cos(x),\at\:x=\frac{3π}{2}
integral of x^4e^{-2x}	\int\:x^{4}e^{-2x}dx
integral from-4 to 2 of x^2+2	\int\:_{-4}^{2}x^{2}+2dx
derivative of (Ax+B/(Cx+d))	\frac{d}{dx}(\frac{Ax+B}{Cx+d})
integral from-1 to 3 of 3x^3	\int\:_{-1}^{3}3x^{3}dx
derivative of 2x^2-x^4	\frac{d}{dx}(2x^{2}-x^{4})
derivative of 5x^2-2x	\frac{d}{dx}(5x^{2}-2x)
limit as x approaches 3 of (x^2-9)/(x+2)	\lim\:_{x\to\:3}(\frac{x^{2}-9}{x+2})
laplacetransform 5*t^3	laplacetransform\:5\cdot\:t^{3}
(1+x^2)y^{''}+2xy^'-2y=0	(1+x^{2})y^{\prime\:\prime\:}+2xy^{\prime\:}-2y=0
y^'+y=1.01cos(10x)	y^{\prime\:}+y=1.01\cos(10x)
integral of sqrt(tan(7x))(sec(7x))^2	\int\:\sqrt{\tan(7x)}(\sec(7x))^{2}dx
limit as x approaches 0 of (3x-2)/(9x+7)	\lim\:_{x\to\:0}(\frac{3x-2}{9x+7})
integral from 0 to x of e^{x^2}	\int\:_{0}^{x}e^{x^{2}}dx
integral of-4te^{-4t}	\int\:-4te^{-4t}dt

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