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Popular Calculus Problems

limit as x approaches 2 of x/(x+1)	\lim\:_{x\to\:2}(\frac{x}{x+1})
integral of (e^{-2x})/2	\int\:\frac{e^{-2x}}{2}dx
integral of 1/(2+5x^6)(30x^5)	\int\:\frac{1}{2+5x^{6}}(30x^{5})dx
integral of 1/(sqrt(25-x^2))	\int\:\frac{1}{\sqrt{25-x^{2}}}dx
tangent of f(x)=9x^2+6x-6	tangent\:f(x)=9x^{2}+6x-6
derivative of 7pix^2	derivative\:7πx^{2}
limit as x approaches 0+of 12e^{-2/x}	\lim\:_{x\to\:0+}(12e^{-\frac{2}{x}})
f(R)=R^3	f(R)=R^{3}
integral of (1+1/x)^{-3} 1/(x^2)	\int\:(1+\frac{1}{x})^{-3}\frac{1}{x^{2}}dx
integral of (y^2)/((y^2+3)^{3/2)}	\int\:\frac{y^{2}}{(y^{2}+3)^{\frac{3}{2}}}dy
limit as h approaches 0 of (sin(9h))/(9h)	\lim\:_{h\to\:0}(\frac{\sin(9h)}{9h})
limit as x approaches 0 of sqrt(x+9)-3	\lim\:_{x\to\:0}(\sqrt{x+9}-3)
derivative of (x^2/(x-8))	\frac{d}{dx}(\frac{x^{2}}{x-8})
integral of (x^2)/(x^2+x+6)	\int\:\frac{x^{2}}{x^{2}+x+6}dx
tangent of sqrt(x)+1/(sqrt(x^3))	tangent\:\sqrt{x}+\frac{1}{\sqrt{x^{3}}}
limit as x approaches 2 of sqrt(x^2-4)	\lim\:_{x\to\:2}(\sqrt{x^{2}-4})
derivative of sin^2(5x^2)	\frac{d}{dx}(\sin^{2}(5x^{2}))
limit as x approaches 1 of x-5	\lim\:_{x\to\:1}(x-5)
limit as x approaches infinity of 1x	\lim\:_{x\to\:\infty\:}(1x)
integral of 1/(xln(x^7))	\int\:\frac{1}{x\ln(x^{7})}dx
integral of e^{2θ}	\int\:e^{2θ}dθ
integral of e^{2x}tan^2(e^{2x})	\int\:e^{2x}\tan^{2}(e^{2x})dx
derivative of 2acos(2x-2bsin(2x))	\frac{d}{dx}(2a\cos(2x)-2b\sin(2x))
derivative of r(2x)/(3x^2-4)	derivative\:r\frac{2x}{3x^{2}-4}
derivative of f(x)=(x^2-2sqrt(x))/x	derivative\:f(x)=\frac{x^{2}-2\sqrt{x}}{x}
derivative of (x^2-2x)^3	derivative\:(x^{2}-2x)^{3}
derivative of in(x^2)	derivative\:in(x^{2})
integral from 0 to c of 10e^{2x}	\int\:_{0}^{c}10e^{2x}dx
integral of (3/(x^3))	\int\:(\frac{3}{x^{3}})dx
d/(dt)(e^{it})	\frac{d}{dt}(e^{it})
(dx)/(dt)=sin(2pi(t+3))	\frac{dx}{dt}=\sin(2π(t+3))
inverse oflaplace 1	inverselaplace\:1
integral of (\sqrt[5]{17}-(x^3)/7)^5x^2	\int\:(\sqrt[5]{17}-\frac{x^{3}}{7})^{5}x^{2}dx
sum from n=3 to infinity of 1/3 (2/5)^n	\sum\:_{n=3}^{\infty\:}\frac{1}{3}(\frac{2}{5})^{n}
integral of 1/(5^{4x)}	\int\:\frac{1}{5^{4x}}dx
derivative of (3cos(x)/(3x^2+3x-1))	\frac{d}{dx}(\frac{3\cos(x)}{3x^{2}+3x-1})
-3y^'+(2y)/x =((y^4))/(x^4)	-3y^{\prime\:}+\frac{2y}{x}=\frac{(y^{4})}{x^{4}}
(dy)/(dx)=(x-y-3)/(x-3)	\frac{dy}{dx}=\frac{x-y-3}{x-3}
inverse oflaplace 1/(0.012s^2+1.55s+50)	inverselaplace\:\frac{1}{0.012s^{2}+1.55s+50}
limit as s approaches 1 of ((2s+3))/s	\lim\:_{s\to\:1}(\frac{(2s+3)}{s})
(dy)/(dx)=2y+3	\frac{dy}{dx}=2y+3
integral from 1 to 8 of (x^2-4x+6)	\int\:_{1}^{8}(x^{2}-4x+6)dx
f(x)=ln(x-x^2)	f(x)=\ln(x-x^{2})
integral of 2x^2-3x	\int\:2x^{2}-3xdx
derivative of (2-x)/8	derivative\:\frac{2-x}{8}
integral of x*e^{3x}	\int\:x\cdot\:e^{3x}dx
(d^2y)/(dx^2)+9y=10cos(2x)	\frac{d^{2}y}{dx^{2}}+9y=10\cos(2x)
derivative of (x^3+8)/x	derivative\:\frac{x^{3}+8}{x}
limit as x approaches 0+of log_{4}(2)	\lim\:_{x\to\:0+}(\log_{4}(2))
derivative of-(81/(\sqrt[3]{x+5)})	\frac{d}{dx}(-\frac{81}{\sqrt[3]{x+5}})
3y^{''}-6y^'+6y=e^xsec(x)	3y^{\prime\:\prime\:}-6y^{\prime\:}+6y=e^{x}\sec(x)
integral of 2arctan(x)	\int\:2\arctan(x)dx
limit as x approaches infinity of 1/(e^{-x)x^5}	\lim\:_{x\to\:\infty\:}(\frac{1}{e^{-x}x^{5}})
derivative of 8^{4x}	\frac{d}{dx}(8^{4x})
(\partial)/(\partial y)(xsqrt(1+y^9))	\frac{\partial\:}{\partial\:y}(x\sqrt{1+y^{9}})
limit as x approaches infinity of a_{n}	\lim\:_{x\to\:\infty\:}(a_{n})
derivative of (6x)/(3-tan(x))	derivative\:\frac{6x}{3-\tan(x)}
integral of 8sin^4(r)cos(r)	\int\:8\sin^{4}(r)\cos(r)dr
integral of x^2sin(4x^3+7)	\int\:x^{2}\sin(4x^{3}+7)dx
derivative of f(x)=18x-3x^2	derivative\:f(x)=18x-3x^{2}
integral of 1/(z^2sqrt(9-z^2))	\int\:\frac{1}{z^{2}\sqrt{9-z^{2}}}dz
inverse oflaplace (4s+2)/(s^2+8s+16)	inverselaplace\:\frac{4s+2}{s^{2}+8s+16}
integral of 1/(x^5+2x^3+x)	\int\:\frac{1}{x^{5}+2x^{3}+x}dx
integral from 0 to 10 of 400-20x	\int\:_{0}^{10}400-20xdx
f(t)=5t	f(t)=5t
integral of 4-y	\int\:4-ydy
(d^3)/(dx^3)((1-2x)/(1+2x))	\frac{d^{3}}{dx^{3}}(\frac{1-2x}{1+2x})
derivative of 4/5 x^{5/4}	\frac{d}{dx}(\frac{4}{5}x^{\frac{5}{4}})
derivative of sin(x)+xcos(x)	derivative\:\sin(x)+x\cos(x)
derivative of 6^{x^2}	\frac{d}{dx}(6^{x^{2}})
derivative of ((6x^2+8x+2)/(sqrt(x)))	\frac{d}{dx}(\frac{(6x^{2}+8x+2)}{\sqrt{x}})
(\partial)/(\partial x)(30y^4sin(2x))	\frac{\partial\:}{\partial\:x}(30y^{4}\sin(2x))
derivative of (x-4)ln(4-x)	derivative\:(x-4)\ln(4-x)
derivative of xsin(4x)	\frac{d}{dx}(x\sin(4x))
tangent of f(x)=cos((pix)/2),\at x=0.4	tangent\:f(x)=\cos(\frac{πx}{2}),\at\:x=0.4
integral of 30e^{-x}	\int\:30e^{-x}dx
(\partial)/(\partial x)(9xy)	\frac{\partial\:}{\partial\:x}(9xy)
limit as x approaches-1+of ln(x+1)	\lim\:_{x\to\:-1+}(\ln(x+1))
derivative of (x-4(x+1)(x+5))	\frac{d}{dx}((x-4)(x+1)(x+5))
derivative of f(x)=(x^3)/(3-x^2)	derivative\:f(x)=\frac{x^{3}}{3-x^{2}}
integral of ((4x-5)(2x-7))/3	\int\:\frac{(4x-5)(2x-7)}{3}dx
(\partial)/(\partial x)(ln(x^2+6y^2+8))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+6y^{2}+8))
(dy)/(dx)=(y+8)	\frac{dy}{dx}=(y+8)
integral of (sec(θ))/(tan(θ))	\int\:\frac{\sec(θ)}{\tan(θ)}dθ
(dy)/(dx)+x*y=-x^2	\frac{dy}{dx}+x\cdot\:y=-x^{2}
derivative of x(x-4^2)	\frac{d}{dx}(x(x-4)^{2})
tangent of 2x^2+3x,\at x=-3	tangent\:2x^{2}+3x,\at\:x=-3
integral of (cos(x))/(8+sin(x))	\int\:\frac{\cos(x)}{8+\sin(x)}dx
limit as x approaches 0 of (1+8x)^{3/x}	\lim\:_{x\to\:0}((1+8x)^{\frac{3}{x}})
integral of (2x+6)5	\int\:(2x+6)5dx
integral of 1/(x^6)	\int\:\frac{1}{x^{6}}dx
derivative of (5+3x-6sqrt(x)/x)	\frac{d}{dx}(\frac{5+3x-6\sqrt{x}}{x})
(-4x+3y-7)dx-(x+1)dy=0	(-4x+3y-7)dx-(x+1)dy=0
(\partial)/(\partial x)(x+xy^2)	\frac{\partial\:}{\partial\:x}(x+xy^{2})
integral of 1/(sin(x))(cos(x))/(sin(x))	\int\:\frac{1}{\sin(x)}\frac{\cos(x)}{\sin(x)}dx
limit as h approaches 0 of ((1+h)3-1)/h	\lim\:_{h\to\:0}(\frac{(1+h)3-1}{h})
limit as x,y approaches (0,0) of ((2x^2y))/(x^2+y^4)	\lim\:_{x,y\to\:(0,0)}(\frac{(2x^{2}y)}{x^{2}+y^{4}})
limit as x approaches 2+of 3-x	\lim\:_{x\to\:2+}(3-x)
derivative of (2^x/(cos(x)))	\frac{d}{dx}(\frac{2^{x}}{\cos(x)})
y^{''}+2y^'+y=64e^{(7t)}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=64e^{(7t)}

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