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Popular Calculus Problems

integral of (9-x^2)/(5x^3+x)	\int\:\frac{9-x^{2}}{5x^{3}+x}dx
derivative of f(x)=((2x+1)/(x+5))(3x-1)	derivative\:f(x)=(\frac{2x+1}{x+5})(3x-1)
(d^2)/(dx^2)(6/(7t^4))	\frac{d^{2}}{dx^{2}}(\frac{6}{7t^{4}})
derivative of x^2ln(2x)	derivative\:x^{2}\ln(2x)
integral of ((sqrt(x)+3)^2)/(2sqrt(x))	\int\:\frac{(\sqrt{x}+3)^{2}}{2\sqrt{x}}dx
integral of (3x^3+4x^2-2x^{-1}+13)	\int\:(3x^{3}+4x^{2}-2x^{-1}+13)dx
laplacetransform t^2cos(5t)	laplacetransform\:t^{2}\cos(5t)
derivative of (sin(x))/(2+cos(x))	derivative\:\frac{\sin(x)}{2+\cos(x)}
taylor sin(5x),x=0	taylor\:\sin(5x),x=0
derivative of 1/(ln(x+1))	derivative\:\frac{1}{\ln(x+1)}
(\partial)/(\partial y)(5x+y)	\frac{\partial\:}{\partial\:y}(5x+y)
d/(da)(sin^4(a)+cos^4(a))	\frac{d}{da}(\sin^{4}(a)+\cos^{4}(a))
integral of (sec(x)tan(x))/(-5+sec(x))	\int\:\frac{\sec(x)\tan(x)}{-5+\sec(x)}dx
limit as x approaches 0+of 9cos(9x)	\lim\:_{x\to\:0+}(9\cos(9x))
integral of (e^x)/(e^x-2)	\int\:\frac{e^{x}}{e^{x}-2}dx
limit as x approaches 0 of-4x^{-3}	\lim\:_{x\to\:0}(-4x^{-3})
derivative of arctan((a^2-x^3/(b^2)))	\frac{d}{dx}(\arctan(\frac{a^{2}-x^{3}}{b^{2}}))
integral from 1 to infinity of x/(x^2+1)	\int\:_{1}^{\infty\:}\frac{x}{x^{2}+1}dx
(\partial)/(\partial y)(xy^2e^{x^2})	\frac{\partial\:}{\partial\:y}(xy^{2}e^{x^{2}})
limit as x approaches-1-of 2x^2-4x+8	\lim\:_{x\to\:-1-}(2x^{2}-4x+8)
(\partial)/(\partial x)(6xy+5yz+xz-48)	\frac{\partial\:}{\partial\:x}(6xy+5yz+xz-48)
16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2	16y^{\prime\:\prime\:}+152y^{\prime\:}+361y=0,y(0)=9,y^{\prime\:}(0)=2
(\partial)/(\partial y)(ln(1+x^2+y))	\frac{\partial\:}{\partial\:y}(\ln(1+x^{2}+y))
integral of (18)/((x^2-1)^2)	\int\:\frac{18}{(x^{2}-1)^{2}}dx
y^'+7x^{-1}y=x^2	y^{\prime\:}+7x^{-1}y=x^{2}
derivative of 10arcsin(e^{x/2})	derivative\:10\arcsin(e^{\frac{x}{2}})
integral of (4x^2)/(x^2+7)	\int\:\frac{4x^{2}}{x^{2}+7}dx
limit as x approaches 3 of 1/(x-2)	\lim\:_{x\to\:3}(\frac{1}{x-2})
y^{''}-y=(e^x)/(1+x^2)	y^{\prime\:\prime\:}-y=\frac{e^{x}}{1+x^{2}}
derivative of log_{e}(7x^{-2})	\frac{d}{dx}(\log_{e}(7x^{-2}))
derivative of x/(sqrt(x^2+5))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+5}})
integral of sin^3(6x)	\int\:\sin^{3}(6x)dx
derivative of ln(2e^{-t}sin(t))	derivative\:\ln(2e^{-t}\sin(t))
tangent of f(x)=x^2+3x+5	tangent\:f(x)=x^{2}+3x+5
(\partial)/(\partial y)(e^{-y})	\frac{\partial\:}{\partial\:y}(e^{-y})
derivative of \sqrt[7]{x}	derivative\:\sqrt[7]{x}
limit as x approaches 1 of 2x-2	\lim\:_{x\to\:1}(2x-2)
tangent of y= 3/x	tangent\:y=\frac{3}{x}
integral of 1/((x^2+16)^3)	\int\:\frac{1}{(x^{2}+16)^{3}}dx
integral of 1/(3x^2+12)	\int\:\frac{1}{3x^{2}+12}dx
integral of u^{-5}(7-u^5+u^{10})	\int\:u^{-5}(7-u^{5}+u^{10})du
(dy)/(dx)-12y=e^{9x}y^2	\frac{dy}{dx}-12y=e^{9x}y^{2}
(\partial)/(\partial x)(4xye^{x-y^2})	\frac{\partial\:}{\partial\:x}(4xye^{x-y^{2}})
limit as x approaches 0 of e^{x^2}-1	\lim\:_{x\to\:0}(e^{x^{2}}-1)
(dy)/(dx)=x^2-y-2,y(0)=1	\frac{dy}{dx}=x^{2}-y-2,y(0)=1
integral of 5x^{3/2}+2sqrt(x)	\int\:5x^{\frac{3}{2}}+2\sqrt{x}dx
integral of (1-2x^2-4/(x^{-3)})x^{-3}	\int\:(1-2x^{2}-\frac{4}{x^{-3}})x^{-3}dx
integral of (7x^2-12x)e^{2x}	\int\:(7x^{2}-12x)e^{2x}dx
limit as x approaches infinity of x/(\sqrt[3]{x^3+7)}	\lim\:_{x\to\:\infty\:}(\frac{x}{\sqrt[3]{x^{3}+7}})
limit as x approaches-2-of-3x^2+2	\lim\:_{x\to\:-2-}(-3x^{2}+2)
y^'= 1/2+1/4 sin(t)-y/(50)	y^{\prime\:}=\frac{1}{2}+\frac{1}{4}\sin(t)-\frac{y}{50}
integral of a/(b^{3θ)}	\int\:\frac{a}{b^{3θ}}dθ
limit as x approaches 0 of (sin(x^0))/x	\lim\:_{x\to\:0}(\frac{\sin(x^{0})}{x})
integral of (sqrt(x^2-64))/(x^2)	\int\:\frac{\sqrt{x^{2}-64}}{x^{2}}dx
limit as x approaches 3 of ((x^3-5x+6)^{40})/((x^4-10x^2+9)^{20)}	\lim\:_{x\to\:3}(\frac{(x^{3}-5x+6)^{40}}{(x^{4}-10x^{2}+9)^{20}})
derivative of y=t(ln(10t))^2	derivative\:y=t(\ln(10t))^{2}
limit as x approaches 0 of 3x-a	\lim\:_{x\to\:0}(3x-a)
3y^{''}-13y^'+4y=8x+30	3y^{\prime\:\prime\:}-13y^{\prime\:}+4y=8x+30
taylor xsin(-2x)pi	taylor\:x\sin(-2x)π
derivative of 8x^2	derivative\:8x^{2}
integral of 5x^2*e^{5x}	\int\:5x^{2}\cdot\:e^{5x}dx
derivative of 1/2 (2t+1)^{-1/2}	derivative\:\frac{1}{2}(2t+1)^{-\frac{1}{2}}
roots ax^2e^{2x}	roots\:ax^{2}e^{2x}
derivative of x^{-1/2}sin(x)	\frac{d}{dx}(x^{-\frac{1}{2}}\sin(x))
sum from n=1 to infinity of 6/(n^2+2n)	\sum\:_{n=1}^{\infty\:}\frac{6}{n^{2}+2n}
integral from 1 to 10 of (21)/(x^3)	\int\:_{1}^{10}\frac{21}{x^{3}}dx
limit as x approaches-1 of 4/((x+1)^2)	\lim\:_{x\to\:-1}(\frac{4}{(x+1)^{2}})
derivative of sin^2((x^2+1/x))	\frac{d}{dx}(\sin^{2}(\frac{x^{2}+1}{x}))
limit as x approaches 4-of 1/(sqrt(4-x))	\lim\:_{x\to\:4-}(\frac{1}{\sqrt{4-x}})
derivative of (11)/((2x^3-5)^4)	derivative\:\frac{11}{(2x^{3}-5)^{4}}
integral of (x^5+2)/(x^2-1)	\int\:\frac{x^{5}+2}{x^{2}-1}dx
derivative of sin(x*cos(x))	\frac{d}{dx}(\sin(x)\cdot\:\cos(x))
y^{''}+9y=2cos(3x),y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+9y=2\cos(3x),y(0)=1,y^{\prime\:}(0)=0
(\partial)/(\partial x)(x^2*e^{-2y})	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:e^{-2y})
(\partial)/(\partial x)(3y^2x)	\frac{\partial\:}{\partial\:x}(3y^{2}x)
(\partial)/(\partial x)(6x^{7y})	\frac{\partial\:}{\partial\:x}(6x^{7y})
derivative of sin(x+sin(7x))	\frac{d}{dx}(\sin(x+\sin(7x)))
derivative of y=(x-1)e^x	derivative\:y=(x-1)e^{x}
sum from n=1 to infinity of 3/(n(n+3))	\sum\:_{n=1}^{\infty\:}\frac{3}{n(n+3)}
derivative of 3/((3-x^8^{3/2)})	\frac{d}{dx}(\frac{3}{(3-x^{8})^{\frac{3}{2}}})
derivative of (36.5/(x^2))	\frac{d}{dx}(\frac{36.5}{x^{2}})
derivative of x^{10}e^{x+10}	\frac{d}{dx}(x^{10}e^{x+10})
integral from 0 to 1 of 5/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{5}{\sqrt{x}(1+x)}dx
(dy)/(dt)=k(80-y)(50-y)	\frac{dy}{dt}=k(80-y)(50-y)
integral of 1/(4cos(2x))	\int\:\frac{1}{4\cos(2x)}dx
limit as x approaches 4 of sqrt(1-2x)	\lim\:_{x\to\:4}(\sqrt{1-2x})
integral from 0 to 1 of te^{2t}	\int\:_{0}^{1}te^{2t}dt
tangent of tan(x),\at x=-pi/3	tangent\:\tan(x),\at\:x=-\frac{π}{3}
integral from 0 to 14 of 10e^x	\int\:_{0}^{14}10e^{x}dx
(\partial)/(\partial x)(xyln(x/y))	\frac{\partial\:}{\partial\:x}(xy\ln(\frac{x}{y}))
limit as x approaches-(3pi)/2-of tan(x)	\lim\:_{x\to\:-\frac{3π}{2}-}(\tan(x))
integral from 1 to b of 1/((x+7)^2)	\int\:_{1}^{b}\frac{1}{(x+7)^{2}}dx
derivative of arccos(x/a)	\frac{d}{dx}(\arccos(\frac{x}{a}))
derivative of y=(9x^2+4x+4)^5	derivative\:y=(9x^{2}+4x+4)^{5}
laplacetransform 3-2e^{-4t}	laplacetransform\:3-2e^{-4t}
integral of (2x^2+5)/(x^2+1)	\int\:\frac{2x^{2}+5}{x^{2}+1}dx
d/(d{y)}(({z})/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{y}}(\frac{{z}}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
derivative of e^{3t^2}	derivative\:e^{3t^{2}}
integral from 0 to sqrt(3 of) 1/(1+x^2)	\int\:_{0}^{\sqrt{3}}\frac{1}{1+x^{2}}dx
integral of (e^{2x})/(e^{2x)+3}	\int\:\frac{e^{2x}}{e^{2x}+3}dx

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