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Popular Calculus Problems

integral of (x^2)/(9+x^6)	\int\:\frac{x^{2}}{9+x^{6}}dx
limit as x approaches 0 of (x^3+6x)/x	\lim\:_{x\to\:0}(\frac{x^{3}+6x}{x})
integral of cos^2(ax)	\int\:\cos^{2}(ax)dx
sum from n=7 to infinity of 1/((n-4)^4)	\sum\:_{n=7}^{\infty\:}\frac{1}{(n-4)^{4}}
integral of ((x-1))/(x^2+5x+6)	\int\:\frac{(x-1)}{x^{2}+5x+6}dx
y^{''}-5/t y^'+(25)/(t^2)y=0	y^{\prime\:\prime\:}-\frac{5}{t}y^{\prime\:}+\frac{25}{t^{2}}y=0
integral of 12sqrt(x)	\int\:12\sqrt{x}dx
integral of (1-3x)^{1/3}	\int\:(1-3x)^{\frac{1}{3}}dx
limit as x approaches pi of tan(2/3 x)	\lim\:_{x\to\:π}(\tan(\frac{2}{3}x))
derivative of f(x)=(x^2)/(2+sqrt(x))	derivative\:f(x)=\frac{x^{2}}{2+\sqrt{x}}
limit as n approaches infinity of n/1	\lim\:_{n\to\:\infty\:}(\frac{n}{1})
integral of e^{3x}cos(4x)	\int\:e^{3x}\cos(4x)dx
derivative of x^{(ln(2)/(1+ln(x))})	\frac{d}{dx}(x^{\frac{\ln(2)}{1+\ln(x)}})
integral of 7/((t-1)sqrt(t^2-2t-48))	\int\:\frac{7}{(t-1)\sqrt{t^{2}-2t-48}}dt
sum from n=0 to infinity of 3^{n-1}	\sum\:_{n=0}^{\infty\:}3^{n-1}
y^'+x/(x^2-9)y=2x	y^{\prime\:}+\frac{x}{x^{2}-9}y=2x
sum from n=3 to infinity}((ln(x))^{n-1 of)/(2^n)	\sum\:_{n=3}^{\infty\:}\frac{(\ln(x))^{n-1}}{2^{n}}
limit as x approaches-9 of (x^2-4)/(x-9)	\lim\:_{x\to\:-9}(\frac{x^{2}-4}{x-9})
limit as x approaches infinity of x^4e^{-x^3}	\lim\:_{x\to\:\infty\:}(x^{4}e^{-x^{3}})
sum from n=0 to infinity of 1/(n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+1}
integral of (sqrt(x^2-16))/(x^3)	\int\:\frac{\sqrt{x^{2}-16}}{x^{3}}dx
tangent of f(x)=(2ln(x))/x ,\at x=1	tangent\:f(x)=\frac{2\ln(x)}{x},\at\:x=1
derivative of (sin(8x)/(e^{4x)})	\frac{d}{dx}(\frac{\sin(8x)}{e^{4x}})
(\partial)/(\partial x)(ln(3y^2-x^3-3))	\frac{\partial\:}{\partial\:x}(\ln(3y^{2}-x^{3}-3))
limit as x approaches 0 of (5^x-13^x)/x	\lim\:_{x\to\:0}(\frac{5^{x}-13^{x}}{x})
limit as x approaches 0 of x*sin(1/x)	\lim\:_{x\to\:0}(x\cdot\:\sin(\frac{1}{x}))
(\partial)/(\partial x)(ln(x)-4)	\frac{\partial\:}{\partial\:x}(\ln(x)-4)
derivative of y^5sin(5x)	\frac{d}{dx}(y^{5}\sin(5x))
(\partial)/(\partial x)(4sin(4x)e^{3x})	\frac{\partial\:}{\partial\:x}(4\sin(4x)e^{3x})
sum from n=1 to infinity of 5/(4^{n-1)}	\sum\:_{n=1}^{\infty\:}\frac{5}{4^{n-1}}
(\partial)/(\partial y)(e^{x^2+y^2})	\frac{\partial\:}{\partial\:y}(e^{x^{2}+y^{2}})
sum from k=1 to infinity of e^{-k}	\sum\:_{k=1}^{\infty\:}e^{-k}
(\partial)/(\partial x)(4xyarcsin(yz))	\frac{\partial\:}{\partial\:x}(4xy\arcsin(yz))
integral of 8/(9tsqrt(81t^2-64))	\int\:\frac{8}{9t\sqrt{81t^{2}-64}}dt
integral of ((tan(x))/(cot(x)))^3	\int\:(\frac{\tan(x)}{\cot(x)})^{3}dx
(sin(sin(x)))^'	(\sin(\sin(x)))^{\prime\:}
derivative of f(x)=x^2e^x	derivative\:f(x)=x^{2}e^{x}
integral of (10)/(x^2+8x+15)	\int\:\frac{10}{x^{2}+8x+15}dx
(\partial)/(\partial x)(ye^y-xe^x)	\frac{\partial\:}{\partial\:x}(ye^{y}-xe^{x})
limit as x approaches 3 of x^2-5x+6	\lim\:_{x\to\:3}(x^{2}-5x+6)
(y^3-2x^2y)dx+(2x^3)dy=0	(y^{3}-2x^{2}y)dx+(2x^{3})dy=0
inverse oflaplace (6s+3)/(s^4+5s^2+4)	inverselaplace\:\frac{6s+3}{s^{4}+5s^{2}+4}
limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36)	\lim\:_{x\to\:-6}(\frac{(4x+3)^{\frac{2}{3}}-9}{x^{2}-36})
integral of pi/3	\int\:\frac{π}{3}
yy^'=xy^2-x-y^2+1	yy^{\prime\:}=xy^{2}-x-y^{2}+1
integral of (11x+20)/(x^2+4x+5)	\int\:\frac{11x+20}{x^{2}+4x+5}dx
f(x)= x/(4+x^2)	f(x)=\frac{x}{4+x^{2}}
derivative of f(t)=7t-2t^2	derivative\:f(t)=7t-2t^{2}
(\partial)/(\partial z)(e^{9xz})	\frac{\partial\:}{\partial\:z}(e^{9xz})
integral of 2sin(npix)	\int\:2\sin(nπx)dx
sum from n=0 to infinity of (6n)/(2n-1)	\sum\:_{n=0}^{\infty\:}\frac{6n}{2n-1}
derivative of (x^2-x^{7/3}^4)	\frac{d}{dx}((x^{2}-x^{\frac{7}{3}})^{4})
10y^'+5y=8e^{6x},y(0)=9	10y^{\prime\:}+5y=8e^{6x},y(0)=9
limit as x approaches 3 of (\|x\|-x)/(3-x)	\lim\:_{x\to\:3}(\frac{\left\|x\right\|-x}{3-x})
y^{''}+(y^')^2+1=0	y^{\prime\:\prime\:}+(y^{\prime\:})^{2}+1=0
integral from-40 to 0 of 1/(sqrt(9-x))	\int\:_{-40}^{0}\frac{1}{\sqrt{9-x}}dx
derivative of y=30e^{-0.0000323x}	derivative\:y=30e^{-0.0000323x}
area 1/8 x,8x, 2/x	area\:\frac{1}{8}x,8x,\frac{2}{x}
integral from 2 to 8 of 5/(4-3x)	\int\:_{2}^{8}\frac{5}{4-3x}dx
integral of (sqrt(1-x^2))	\int\:(\sqrt{1-x^{2}})dx
(x^2+y)dx-(x)dy=0	(x^{2}+y)dx-(x)dy=0
limit as x approaches 1 of (3x^2+5x-8)/(x^2-1)	\lim\:_{x\to\:1}(\frac{3x^{2}+5x-8}{x^{2}-1})
integral of (-2/(sqrt(7-7x^2)))	\int\:(-\frac{2}{\sqrt{7-7x^{2}}})dx
integral of 1/((2x+6)^2)	\int\:\frac{1}{(2x+6)^{2}}dx
integral of (x+1)sqrt(2x-1)	\int\:(x+1)\sqrt{2x-1}dx
(dx)/(dt)=x^2,x(0)=1	\frac{dx}{dt}=x^{2},x(0)=1
integral of-6x^{-7}	\int\:-6x^{-7}dx
(dy)/(dx)+((1-y^2)/(1-x^2))^{1/2}=0	\frac{dy}{dx}+(\frac{1-y^{2}}{1-x^{2}})^{\frac{1}{2}}=0
(dy)/(dx)=9y	\frac{dy}{dx}=9y
derivative of G(t)=(1-3t)/(4+t)	derivative\:G(t)=\frac{1-3t}{4+t}
integral of (x^2)/(5x^3+8)	\int\:\frac{x^{2}}{5x^{3}+8}dx
tangent of f(x)=3e^x+x,(0,3)	tangent\:f(x)=3e^{x}+x,(0,3)
integral of (7x(x^6-1/7))	\int\:(7x(x^{6}-\frac{1}{7}))dx
inverse oflaplace 1/((s^2+5))	inverselaplace\:\frac{1}{(s^{2}+5)}
derivative of f(x)=(1-4x)/(1+4x)	derivative\:f(x)=\frac{1-4x}{1+4x}
(\partial)/(\partial y)(4x^3y^3+2)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3}+2)
xdy-ydx=(xy)^{1/2}	xdy-ydx=(xy)^{\frac{1}{2}}
(\partial)/(\partial x)(6e^{x^5y})	\frac{\partial\:}{\partial\:x}(6e^{x^{5}y})
integral from 0 to 1 of (x-1)/(sqrt(x))	\int\:_{0}^{1}\frac{x-1}{\sqrt{x}}dx
tangent of g(x)=-3x^2+5x-6	tangent\:g(x)=-3x^{2}+5x-6
derivative of sqrt(6x)	derivative\:\sqrt{6x}
integral of ((x-1))/2	\int\:\frac{(x-1)}{2}dx
(8+x)y^'=7y	(8+x)y^{\prime\:}=7y
(\partial)/(\partial x)(ln(x^2+y^4)-z)	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{4})-z)
(\partial)/(\partial x)((2y)/(9x^2+y^2+9))	\frac{\partial\:}{\partial\:x}(\frac{2y}{9x^{2}+y^{2}+9})
derivative of ln(x^2+9)	derivative\:\ln(x^{2}+9)
derivative of 2e^{-x^2}	\frac{d}{dx}(2e^{-x^{2}})
integral of 6cos(3x)	\int\:6\cos(3x)dx
integral of 1/(x(1-0.0004x))	\int\:\frac{1}{x(1-0.0004x)}dx
derivative of acos(2x+bsin(2x))	\frac{d}{dx}(a\cos(2x)+b\sin(2x))
derivative of asin(x)	\frac{d}{dx}(a\sin(x))
y^{''}+4y^'+4y=0,y(0)=1,y^'(0)=-4	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=0,y(0)=1,y^{\prime\:}(0)=-4
integral of tan(2xse)c^22x	\int\:\tan(2xse)c^{2}2xdx
tangent of y=3x-2x^2,(-3,-27)	tangent\:y=3x-2x^{2},(-3,-27)
limit as x approaches 0+of x+1	\lim\:_{x\to\:0+}(x+1)
(dy)/(dx)=e^{2y}sin(x)	\frac{dy}{dx}=e^{2y}\sin(x)
integral of sqrt(x)-6cos(x)	\int\:\sqrt{x}-6\cos(x)dx
sum from n=1 to infinity of (x^n)/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{10^{n}}
integral from 0 to 1 of sqrt(36t^2+9t^4)	\int\:_{0}^{1}\sqrt{36t^{2}+9t^{4}}dt
y^'=(sin(2x))/(e^y)	y^{\prime\:}=\frac{\sin(2x)}{e^{y}}

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