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Popular Calculus Problems

integral from 2 to 5 of x^4ln(2x)	\int\:_{2}^{5}x^{4}\ln(2x)dx
integral from 0 to 18 of sqrt(t^2+2t+1)	\int\:_{0}^{18}\sqrt{t^{2}+2t+1}dt
(\partial)/(\partial y)(3y-e^{sin(x)})	\frac{\partial\:}{\partial\:y}(3y-e^{\sin(x)})
limit as x approaches 3-of (6x)/(2x-5)	\lim\:_{x\to\:3-}(\frac{6x}{2x-5})
integral from 4 to infinity of (ln(x))/x	\int\:_{4}^{\infty\:}\frac{\ln(x)}{x}dx
d/(dθ)(1/4 sin^2(2θ))	\frac{d}{dθ}(\frac{1}{4}\sin^{2}(2θ))
7y^'+y=5t^2	7y^{\prime\:}+y=5t^{2}
derivative of e^{x^3-x}	\frac{d}{dx}(e^{x^{3}-x})
sum from n=0 to infinity of e^{-(3n)/2}	\sum\:_{n=0}^{\infty\:}e^{-\frac{3n}{2}}
d/(dx_{0)}(x_{0})	\frac{d}{dx_{0}}(x_{0})
limit as x approaches 2 of e^{3/(2-x)}	\lim\:_{x\to\:2}(e^{\frac{3}{2-x}})
integral of 4x^2+2+5/(x^2+1)	\int\:4x^{2}+2+\frac{5}{x^{2}+1}dx
integral of xe^{-18x}	\int\:xe^{-18x}dx
integral of 6x^2sin(4x)	\int\:6x^{2}\sin(4x)dx
integral of 1/(4x^{1/2)}	\int\:\frac{1}{4x^{\frac{1}{2}}}dx
x^2y^{''}-x(x+2)y^'+(x+2)y=0	x^{2}y^{\prime\:\prime\:}-x(x+2)y^{\prime\:}+(x+2)y=0
derivative of x+7x-7	derivative\:x+7x-7
limit as x approaches infinity of 3+x	\lim\:_{x\to\:\infty\:}(3+x)
9y^{''}+6y^'+y=e^{-1/3 t}	9y^{\prime\:\prime\:}+6y^{\prime\:}+y=e^{-\frac{1}{3}t}
derivative of 1/(x^2sqrt(x))	\frac{d}{dx}(\frac{1}{x^{2}\sqrt{x}})
integral of 1/((1-x^2)^{0.5)}	\int\:\frac{1}{(1-x^{2})^{0.5}}dx
integral of sqrt((x^2-3)/(x^8))	\int\:\sqrt{\frac{x^{2}-3}{x^{8}}}dx
integral of 2x^2(-x^3+3)^5	\int\:2x^{2}(-x^{3}+3)^{5}dx
(\partial)/(\partial t)(3arcsin(t))	\frac{\partial\:}{\partial\:t}(3\arcsin(t))
(dy)/(dx)=-(1+y)^4	\frac{dy}{dx}=-(1+y)^{4}
derivative of 1/2 x+4	\frac{d}{dx}(\frac{1}{2}x+4)
(\partial)/(\partial y)(2xy+3y)	\frac{\partial\:}{\partial\:y}(2xy+3y)
integral of 2x+1	\int\:2x+1dx
integral of x^2sqrt(x^{3+1)}	\int\:x^{2}\sqrt{x^{3+1}}dx
limit as x approaches-1 of (x-1)/(x^1-1)	\lim\:_{x\to\:-1}(\frac{x-1}{x^{1}-1})
integral of (x^3+x-2)/(x^4+2x^3+3x^2)	\int\:\frac{x^{3}+x-2}{x^{4}+2x^{3}+3x^{2}}dx
tangent of (x^2+y^2)^2=4x^2y,(-1,1)	tangent\:(x^{2}+y^{2})^{2}=4x^{2}y,(-1,1)
integral from 1 to 10 of (sqrt(x^2-1))/x	\int\:_{1}^{10}\frac{\sqrt{x^{2}-1}}{x}dx
derivative of ln(2pix^2)	\frac{d}{dx}(\ln(2πx^{2}))
integral of (e^{6x})/(e^{6x)sin^2(4x)}	\int\:\frac{e^{6x}}{e^{6x}\sin^{2}(4x)}dx
limit as x approaches 2 of (1/x)^3	\lim\:_{x\to\:2}((\frac{1}{x})^{3})
derivative of 3/8 x^{2/3}	\frac{d}{dx}(\frac{3}{8}x^{\frac{2}{3}})
derivative of 2/(sqrt(x-3))	\frac{d}{dx}(\frac{2}{\sqrt{x-3}})
derivative of ((x^2+1/(x^2-1))^3)	\frac{d}{dx}((\frac{x^{2}+1}{x^{2}-1})^{3})
(\partial)/(\partial x)(e^{x+7y})	\frac{\partial\:}{\partial\:x}(e^{x+7y})
derivative of y=(x^2+7x+2)^3	derivative\:y=(x^{2}+7x+2)^{3}
y^'=8*(2+y)/x ,y(1)=8	y^{\prime\:}=8\cdot\:\frac{2+y}{x},y(1)=8
derivative of y=6cot(3x)	derivative\:y=6\cot(3x)
derivative of (x-6(5x+1))	\frac{d}{dx}((x-6)(5x+1))
derivative of f(x)=(-x^2-6)/((x^2-6)^2)	derivative\:f(x)=\frac{-x^{2}-6}{(x^{2}-6)^{2}}
(\partial ^2)/(\partial y^2)((xy)/(x-y))	\frac{\partial\:^{2}}{\partial\:y^{2}}(\frac{xy}{x-y})
integral of (3+x)/(1-x^2)	\int\:\frac{3+x}{1-x^{2}}dx
y=(5-x^2)^5	y=(5-x^{2})^{5}
integral of sqrt(x^2+6x+13)	\int\:\sqrt{x^{2}+6x+13}dx
tangent of f(x)= 1/(x^3),\at x=1	tangent\:f(x)=\frac{1}{x^{3}},\at\:x=1
(\partial)/(\partial x)(y^6sin(5x))	\frac{\partial\:}{\partial\:x}(y^{6}\sin(5x))
derivative of arctan(4/x)	derivative\:\arctan(\frac{4}{x})
(dy}{dx}+y=\frac{e^x)/y	\frac{dy}{dx}+y=\frac{e^{x}}{y}
integral from 3 to 4 of e^{3-x}	\int\:_{3}^{4}e^{3-x}dx
integral of 1/(6x^6)	\int\:\frac{1}{6x^{6}}dx
area ln(x), 4/x ,1,3	area\:\ln(x),\frac{4}{x},1,3
derivative of cos(x+cos^2(x))	\frac{d}{dx}(\cos(x)+\cos^{2}(x))
integral of e^{t/2}	\int\:e^{\frac{t}{2}}dt
(d^2)/(dx^2)((x^2)/(8+x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{8+x})
integral of sin^2(2x)cos(3x)	\int\:\sin^{2}(2x)\cos(3x)dx
(\partial)/(\partial x)(e^{xy}cos(x+y))	\frac{\partial\:}{\partial\:x}(e^{xy}\cos(x+y))
derivative of bxe^x	\frac{d}{dx}(bxe^{x})
(\partial)/(\partial x)((2x^2y)/(5+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{2x^{2}y}{5+x^{2}y^{2}})
derivative of ((x^2+3^5+x)^2)	\frac{d}{dx}(((x^{2}+3)^{5}+x)^{2})
derivative of ln(5+x)	derivative\:\ln(5+x)
(\partial)/(\partial x)(8y^5+8y^2x^7)	\frac{\partial\:}{\partial\:x}(8y^{5}+8y^{2}x^{7})
derivative of (20/(x+1))	\frac{d}{dx}(\frac{20}{x+1})
limit as x approaches+0 of 7/x-7/(x^2-x)	\lim\:_{x\to\:+0}(\frac{7}{x}-\frac{7}{x^{2}-x})
limit as x approaches 0 of 2-1/(x^3)	\lim\:_{x\to\:0}(2-\frac{1}{x^{3}})
limit as x approaches 0 of sqrt(2-x)	\lim\:_{x\to\:0}(\sqrt{2-x})
limit as x approaches 5 of 2x+1	\lim\:_{x\to\:5}(2x+1)
(\partial)/(\partial y)(xy-2/x-4/y+8)	\frac{\partial\:}{\partial\:y}(xy-\frac{2}{x}-\frac{4}{y}+8)
integral of (9e^x-3e^{-x})^2	\int\:(9e^{x}-3e^{-x})^{2}dx
integral of+e^xcos(+(x))	\int\:+e^{x}\cos(+(x))dx
limit as x approaches 0+of (x^2)/7-6/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{7}-\frac{6}{x})
derivative of (sech(2x)^2)	\frac{d}{dx}((\sech(2x))^{2})
derivative of ln((tan(x)^{1/x}))	\frac{d}{dx}(\ln((\tan(x))^{\frac{1}{x}}))
derivative of y=16\sqrt[4]{4x^4+4}	derivative\:y=16\sqrt[4]{4x^{4}+4}
limit as x approaches 2 of 5x^3-7^2+6	\lim\:_{x\to\:2}(5x^{3}-7^{2}+6)
simplify (e^x)/(sqrt(x))	simplify\:\frac{e^{x}}{\sqrt{x}}
(\partial)/(\partial x)(y^3-ln(x))	\frac{\partial\:}{\partial\:x}(y^{3}-\ln(x))
integral of 4x*e^x	\int\:4x\cdot\:e^{x}dx
(\partial}{\partial x}(-\frac{9x)/y)	\frac{\partial\:}{\partial\:x}(-\frac{9x}{y})
-x^'-x/(0.00022)+13364=0	-x^{\prime\:}-\frac{x}{0.00022}+13364=0
derivative of ln((x+2/(x+1)))	\frac{d}{dx}(\ln(\frac{x+2}{x+1}))
integral of (a+bx^8)/(sqrt(9ax+bx^9))	\int\:\frac{a+bx^{8}}{\sqrt{9ax+bx^{9}}}dx
limit as x approaches infinity of b^x	\lim\:_{x\to\:\infty\:}(b^{x})
laplacetransform cos(t-pi/6)	laplacetransform\:\cos(t-\frac{π}{6})
integral of-cos(x)+sin(x)	\int\:-\cos(x)+\sin(x)dx
derivative of 2/3 x	\frac{d}{dx}(\frac{2}{3}x)
derivative of \sqrt[3]{5x^7+6x^6}	derivative\:\sqrt[3]{5x^{7}+6x^{6}}
(5du)/(dt)=u^2	\frac{5du}{dt}=u^{2}
derivative of cos(1/x)	derivative\:\cos(\frac{1}{x})
limit as t approaches 2+of (t+2)/(t^2-4)	\lim\:_{t\to\:2+}(\frac{t+2}{t^{2}-4})
derivative of 6sin(x)	derivative\:6\sin(x)
derivative of 1/((4-x^2))	derivative\:\frac{1}{(4-x^{2})}
integral of 1/(yln^2(y))	\int\:\frac{1}{y\ln^{2}(y)}dy
integral of ((x^2+9))/(x^2+2x+3)	\int\:\frac{(x^{2}+9)}{x^{2}+2x+3}dx
y^{''}+y^'=e^x	y^{\prime\:\prime\:}+y^{\prime\:}=e^{x}
integral of 1/(x^{-1)}	\int\:\frac{1}{x^{-1}}dx

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