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Popular Calculus Problems

derivative of x^7ln(3x)	\frac{d}{dx}(x^{7}\ln(3x))
integral from 1 to 2 of 5r^2ln(r)	\int\:_{1}^{2}5r^{2}\ln(r)dr
derivative of (-3cos(2x-sin(3x))^2)	\frac{d}{dx}((-3\cos(2x)-\sin(3x))^{2})
derivative of (4x)/(9-cot(x))	derivative\:\frac{4x}{9-\cot(x)}
limit as t approaches 0 of e^{-4t}	\lim\:_{t\to\:0}(e^{-4t})
integral of ((ln(x))^{17})/x	\int\:\frac{(\ln(x))^{17}}{x}dx
(dy)/(dx)=(4y^3)/(x^2)	\frac{dy}{dx}=\frac{4y^{3}}{x^{2}}
integral of (4x+4)/(x^2(x^2+1))	\int\:\frac{4x+4}{x^{2}(x^{2}+1)}dx
derivative of xln(x+x)	\frac{d}{dx}(x\ln(x)+x)
integral of ye^{2xy}+x	\int\:ye^{2xy}+xdx
limit as x approaches 0 of (e^{-7x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{-7x}-1}{x})
y^'=x+5y	y^{\prime\:}=x+5y
y^'=x^2-1	y^{\prime\:}=x^{2}-1
limit as x approaches-pi of e^{tan(x)}	\lim\:_{x\to\:-π}(e^{\tan(x)})
area f(x)=-x^2+3x-1,-3,1	area\:f(x)=-x^{2}+3x-1,-3,1
y^{''}-y^'-2y=-4e^{3t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-4e^{3t}
derivative of ((ax+b)/(cx+d))	\frac{d}{dx}(\frac{(ax+b)}{cx+d})
taylor 1/(x-1),11	taylor\:\frac{1}{x-1},11
derivative of y=x^7f(x)	derivative\:y=x^{7}f(x)
(\partial)/(\partial x)(x^{2.75}y^{2.5})	\frac{\partial\:}{\partial\:x}(x^{2.75}y^{2.5})
derivative of 6cos(t)	derivative\:6\cos(t)
integral of (x+1)^{-2}	\int\:(x+1)^{-2}dx
derivative of sqrt(5x+11)	\frac{d}{dx}(\sqrt{5x+11})
integral of sqrt(x^2+6x)	\int\:\sqrt{x^{2}+6x}dx
(dy)/(dt)=y(10^{-1}-10^{-7}y),y(0)=4000	\frac{dy}{dt}=y(10^{-1}-10^{-7}y),y(0)=4000
derivative of (x^2+2x+1/x)	\frac{d}{dx}(\frac{x^{2}+2x+1}{x})
integral of (2x^2)/(sqrt(1-6x^3))	\int\:\frac{2x^{2}}{\sqrt{1-6x^{3}}}dx
integral of 1/(x*sqrt(9-x^2))	\int\:\frac{1}{x\cdot\:\sqrt{9-x^{2}}}dx
integral of 1/(xln^3(x))	\int\:\frac{1}{x\ln^{3}(x)}dx
(\partial)/(\partial x)(tan(3x-5y))	\frac{\partial\:}{\partial\:x}(\tan(3x-5y))
(\partial)/(\partial x)(y^2-1)	\frac{\partial\:}{\partial\:x}(y^{2}-1)
integral of (sqrt(x))/(sqrt(x)-1)	\int\:\frac{\sqrt{x}}{\sqrt{x}-1}dx
sum from n=0 to infinity of (7/18)^n	\sum\:_{n=0}^{\infty\:}(\frac{7}{18})^{n}
sec(x)(dy)/(dx)+y=1	\sec(x)\frac{dy}{dx}+y=1
limit as x approaches 3 of (1.5)/(3-1.5)	\lim\:_{x\to\:3}(\frac{1.5}{3-1.5})
integral from-1 to 1 of \sqrt[3]{t}-2	\int\:_{-1}^{1}\sqrt[3]{t}-2dt
(dy)/(dx)=4cos(x)-ycos(x)	\frac{dy}{dx}=4\cos(x)-y\cos(x)
integral of (7e^{-0.5x})	\int\:(7e^{-0.5x})dx
derivative of xsqrt(144-x^2)	derivative\:x\sqrt{144-x^{2}}
integral of (cos(x)+sin(2x))/(sin(x))	\int\:\frac{\cos(x)+\sin(2x)}{\sin(x)}dx
derivative of (x+4^{-2})	\frac{d}{dx}((x+4)^{-2})
x(dy)/(dx)+(3x+1)y=e^{(-3x)},y(1)=e^7	x\frac{dy}{dx}+(3x+1)y=e^{(-3x)},y(1)=e^{7}
(\partial)/(\partial x)(x+y)	\frac{\partial\:}{\partial\:x}(x+y)
integral of e^{3-z}sin(2+z)	\int\:e^{3-z}\sin(2+z)dz
inverse oflaplace e^{-3s}	inverselaplace\:e^{-3s}
sum from n=0 to infinity of (x^n)/(n5^n)	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{n5^{n}}
integral of (2x+1)/(e^{2x+1)}	\int\:\frac{2x+1}{e^{2x+1}}dx
integral of x(e^{2x})	\int\:x(e^{2x})dx
integral of (ax^2-b)^5x	\int\:(ax^{2}-b)^{5}xdx
derivative of arccot(x)	derivative\:\arccot(x)
derivative of 2^{sin(1/x})	\frac{d}{dx}(2^{\sin(\frac{1}{x})})
limit as x approaches 0 of x/(sin(x+pi))	\lim\:_{x\to\:0}(\frac{x}{\sin(x+π)})
derivative of (2000/x)	\frac{d}{dx}(\frac{2000}{x})
(d^2)/(dx^2)(e^{-5x^2})	\frac{d^{2}}{dx^{2}}(e^{-5x^{2}})
limit as x approaches+0 of 6sin(x)ln(x)	\lim\:_{x\to\:+0}(6\sin(x)\ln(x))
integral from-2 to 3 of (x-4\|x\|)	\int\:_{-2}^{3}(x-4\left\|x\right\|)dx
integral of ((tan^3(x))(sec^4(x)))	\int\:((\tan^{3}(x))(\sec^{4}(x)))dx
(\partial)/(\partial x)(3x^2-3y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}-3y^{2})
limit as x approaches-4 of-5x	\lim\:_{x\to\:-4}(-5x)
derivative of 2xsqrt(1-x^2)	\frac{d}{dx}(2x\sqrt{1-x^{2}})
x^2y^{''}-5xy^'+8y=0	x^{2}y^{\prime\:\prime\:}-5xy^{\prime\:}+8y=0
tangent of f(x)=2sin(x)+1,\at x=-pi/2	tangent\:f(x)=2\sin(x)+1,\at\:x=-\frac{π}{2}
integral of 5xe^{x^2}	\int\:5xe^{x^{2}}dx
limit as x approaches 0 of ((x-2)^2-4)/x	\lim\:_{x\to\:0}(\frac{(x-2)^{2}-4}{x})
derivative of 3x^2-x	\frac{d}{dx}(3x^{2}-x)
integral of ((4x^8-6x^4))/((2x^6))	\int\:\frac{(4x^{8}-6x^{4})}{(2x^{6})}dx
y^'=(1+x)/(xy^{15)},y(1)=5	y^{\prime\:}=\frac{1+x}{xy^{15}},y(1)=5
integral of csc^2(x/pi)	\int\:\csc^{2}(\frac{x}{π})dx
integral of sin(3x)ln(sin(3x))	\int\:\sin(3x)\ln(\sin(3x))dx
integral from 3 to 6 of x^2	\int\:_{3}^{6}x^{2}dx
integral of (x^3+36)/(x^2+36)	\int\:\frac{x^{3}+36}{x^{2}+36}dx
derivative of 10+1/4 sin(10pix)	\frac{d}{dx}(10+\frac{1}{4}\sin(10πx))
integral of (ln^3(x))/2	\int\:\frac{\ln^{3}(x)}{2}dx
tangent of y=sqrt(x^3+1),(2,3)	tangent\:y=\sqrt{x^{3}+1},(2,3)
limit as x approaches 0 of xcot(3/5 x)	\lim\:_{x\to\:0}(x\cot(\frac{3}{5}x))
derivative of sin(arccos(x))	\frac{d}{dx}(\sin(\arccos(x)))
y^{''}-y^'+y=4sin(t)	y^{\prime\:\prime\:}-y^{\prime\:}+y=4\sin(t)
(\partial}{\partial x}(x^2e^{3x}y+\frac{e^{3x}y^3)/3)	\frac{\partial\:}{\partial\:x}(x^{2}e^{3x}y+\frac{e^{3x}y^{3}}{3})
integral of cos^3(pix)	\int\:\cos^{3}(πx)dx
derivative of f(x)= 1/(13x^2)+1/(11x)	derivative\:f(x)=\frac{1}{13x^{2}}+\frac{1}{11x}
derivative of (5x-1(4x-6)^{-1})	\frac{d}{dx}((5x-1)(4x-6)^{-1})
limit as n approaches infinity+of 1+1/n	\lim\:_{n\to\:\infty\:+}(1+\frac{1}{n})
(\partial)/(\partial y)((ye^x)/(xe^y))	\frac{\partial\:}{\partial\:y}(\frac{ye^{x}}{xe^{y}})
integral of (x^2)/(x^2-9)	\int\:\frac{x^{2}}{x^{2}-9}dx
derivative of-4^3	\frac{d}{dx}(-4^{3})
derivative of y=arccos(9/x)	derivative\:y=\arccos(\frac{9}{x})
tangent of f(x)=4x-x^2	tangent\:f(x)=4x-x^{2}
derivative of 50x	\frac{d}{dx}(50x)
integral from 25 to 50 of 10	\int\:_{25}^{50}10dx
tangent of 6x^2-3x+4	tangent\:6x^{2}-3x+4
integral of (sqrt(x+6))/(x-3)	\int\:\frac{\sqrt{x+6}}{x-3}dx
2x(y+1)-yy^'=0	2x(y+1)-yy^{\prime\:}=0
integral from-2 to 2 of 1/(x^2+4x+13)	\int\:_{-2}^{2}\frac{1}{x^{2}+4x+13}dx
integral of xe-x^2	\int\:xe-x^{2}dx
derivative of f(x)=(8-x)^3	derivative\:f(x)=(8-x)^{3}
derivative of 8sin^2(x)	\frac{d}{dx}(8\sin^{2}(x))
(dx)/(dt)=0.6-3/500 x	\frac{dx}{dt}=0.6-\frac{3}{500}x
integral of (4+x^7)^37x^6	\int\:(4+x^{7})^{3}7x^{6}dx
derivative of 5x^2cos(3x)	derivative\:5x^{2}\cos(3x)
y^{''}-7/t y^'+(32)/(t^2)y=0	y^{\prime\:\prime\:}-\frac{7}{t}y^{\prime\:}+\frac{32}{t^{2}}y=0

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