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Popular Calculus Problems

derivative of (3/4 x)^3	derivative\:(\frac{3}{4}x)^{3}
integral of (49)/(x^3-7x^2)	\int\:\frac{49}{x^{3}-7x^{2}}dx
(dy)/(dx)+12y=5	\frac{dy}{dx}+12y=5
derivative of (cos(x)x)	\frac{d}{dx}((\cos(x))x)
x^2(dy)/(dx)=y-xy,y(-1)=-2	x^{2}\frac{dy}{dx}=y-xy,y(-1)=-2
derivative of f(x)=ln(x^3+10)	derivative\:f(x)=\ln(x^{3}+10)
integral of x^{7/5}	\int\:x^{\frac{7}{5}}dx
integral of (x^3)/(sqrt(49+x^2))	\int\:\frac{x^{3}}{\sqrt{49+x^{2}}}dx
f(x)=arcsec(6x)	f(x)=\arcsec(6x)
integral of 3/(sqrt(1-2x))	\int\:\frac{3}{\sqrt{1-2x}}dx
taylor e^{x^5},0	taylor\:e^{x^{5}},0
limit as x approaches 1 of x^2-4	\lim\:_{x\to\:1}(x^{2}-4)
integral of (3e^{2x})/(e^{2x)+9e^x+18}	\int\:\frac{3e^{2x}}{e^{2x}+9e^{x}+18}dx
limit as x approaches 0 of (1-2x)^{1/x}	\lim\:_{x\to\:0}((1-2x)^{\frac{1}{x}})
integral from 4 to 7 of f(x)	\int\:_{4}^{7}f(x)dx
integral of 3/(2sqrt(x)(1+x))	\int\:\frac{3}{2\sqrt{x}(1+x)}dx
derivative of (2x/(5-cot(x)))	\frac{d}{dx}(\frac{2x}{5-\cot(x)})
integral of cos^9(θ)sin(θ)	\int\:\cos^{9}(θ)\sin(θ)dθ
integral of 1/(3-2x^2)	\int\:\frac{1}{3-2x^{2}}dx
derivative of sin(x)ln(5x)	derivative\:\sin(x)\ln(5x)
y^'=e^{2x}+y-2	y^{\prime\:}=e^{2x}+y-2
integral of x^2e^{-7x}	\int\:x^{2}e^{-7x}dx
(\partial)/(\partial s)(rsin(s))	\frac{\partial\:}{\partial\:s}(r\sin(s))
2y^{''}+y^'-y=0	2y^{\prime\:\prime\:}+y^{\prime\:}-y=0
derivative of sqrt(2e^{x^3)+1}	derivative\:\sqrt{2e^{x^{3}}+1}
d/(dy)(2xe^{xy}+x^2ye^{xy})	\frac{d}{dy}(2xe^{xy}+x^{2}ye^{xy})
(\partial)/(\partial y)(y^2-cos(xy))	\frac{\partial\:}{\partial\:y}(y^{2}-\cos(xy))
limit as x approaches 0.99 of 2x^2-5x+1	\lim\:_{x\to\:0.99}(2x^{2}-5x+1)
integral of 2tan(x)	\int\:2\tan(x)dx
integral of (1-cot(x))csc^2(x)	\int\:(1-\cot(x))\csc^{2}(x)dx
d/(dθ)(-6sin(θ))	\frac{d}{dθ}(-6\sin(θ))
derivative of-1/((2x+8^{3/2)})	\frac{d}{dx}(-\frac{1}{(2x+8)^{\frac{3}{2}}})
integral of+1/(x^2)	\int\:+\frac{1}{x^{2}}dx
derivative of (sqrt(x)/(x+5))	\frac{d}{dx}(\frac{\sqrt{x}}{x+5})
d/(dt)(cos(2t))	\frac{d}{dt}(\cos(2t))
y^{''}-2y^'+y=x^2-1	y^{\prime\:\prime\:}-2y^{\prime\:}+y=x^{2}-1
y^'+4y=e^{-t}-4	y^{\prime\:}+4y=e^{-t}-4
derivative of 3/(2sqrt(3x))	\frac{d}{dx}(\frac{3}{2\sqrt{3x}})
tangent of y=(sqrt(5))^x,\at x=6	tangent\:y=(\sqrt{5})^{x},\at\:x=6
limit as x approaches-2 of (-1)/((x+2))	\lim\:_{x\to\:-2}(\frac{-1}{(x+2)})
derivative of (2x-1^3(x+1)^5)	\frac{d}{dx}((2x-1)^{3}(x+1)^{5})
derivative of 1/5	\frac{d}{dx}(\frac{1}{5})
derivative of (3-sqrt(2x+5))/(x-2)	derivative\:\frac{3-\sqrt{2x+5}}{x-2}
limit as x approaches 0 of x^2+2x+1	\lim\:_{x\to\:0}(x^{2}+2x+1)
t^2y^{''}+3ty^'+y= 1/t	t^{2}y^{\prime\:\prime\:}+3ty^{\prime\:}+y=\frac{1}{t}
integral from 0 to 1 of sqrt(x)-x^2	\int\:_{0}^{1}\sqrt{x}-x^{2}dx
limit as x approaches 0 of 1/(3+x)-1/3	\lim\:_{x\to\:0}(\frac{1}{3+x}-\frac{1}{3})
integral of sqrt(6+7t^2)	\int\:\sqrt{6+7t^{2}}dt
limit as x approaches 1+of ((x))/(ln(x))	\lim\:_{x\to\:1+}(\frac{(x)}{\ln(x)})
(dy)/(dx)=7xe^{4y}	\frac{dy}{dx}=7xe^{4y}
integral of x(x-1)^8	\int\:x(x-1)^{8}dx
tangent of 4x(3-2x)^5,\at 2	tangent\:4x(3-2x)^{5},\at\:2
integral of (a+bx)^n	\int\:(a+bx)^{n}dx
integral of (sin(x))	\int\:(\sin(x))dx
integral of arctan(2y)	\int\:\arctan(2y)dy
derivative of y=ln((1+e^x)/(1-e^x))	derivative\:y=\ln(\frac{1+e^{x}}{1-e^{x}})
(dy)/(dx)=-(y^2)/(1+y^2)e^{(-x)}	\frac{dy}{dx}=-\frac{y^{2}}{1+y^{2}}e^{(-x)}
sum from n=1 to infinity of (2n)/(7n-2)	\sum\:_{n=1}^{\infty\:}\frac{2n}{7n-2}
integral of 1/(sqrt(1+cos(x)))	\int\:\frac{1}{\sqrt{1+\cos(x)}}dx
limit as x approaches 0 of 1/x+1/(x^2)	\lim\:_{x\to\:0}(\frac{1}{x}+\frac{1}{x^{2}})
sum from n=1 to infinity of (2n)!	\sum\:_{n=1}^{\infty\:}(2n)!
limit as n approaches 0 of ln(n)	\lim\:_{n\to\:0}(\ln(n))
integral of x/(x^2+8)	\int\:\frac{x}{x^{2}+8}dx
derivative of 8x^{3/2}+6x^{1/2}+4^{-1/2}	derivative\:8x^{\frac{3}{2}}+6x^{\frac{1}{2}}+4^{-\frac{1}{2}}
tangent of \sqrt[3]{x},\at x=8	tangent\:\sqrt[3]{x},\at\:x=8
(\partial)/(\partial y)(3xy^2e^{4yz})	\frac{\partial\:}{\partial\:y}(3xy^{2}e^{4yz})
limit as x approaches 0+of tan^x(8x)	\lim\:_{x\to\:0+}(\tan^{x}(8x))
tangent of f(x)=x^2,(-1,1)	tangent\:f(x)=x^{2},(-1,1)
integral of xcos(2x^2+7)	\int\:x\cos(2x^{2}+7)dx
limit as h approaches 0 of ((2.7^h-1))/h	\lim\:_{h\to\:0}(\frac{(2.7^{h}-1)}{h})
integral of sin^{-2}(x)cos^3(x)	\int\:\sin^{-2}(x)\cos^{3}(x)dx
integral of 3sqrt(t)	\int\:3\sqrt{t}dt
derivative of 12x^2-2x^3	\frac{d}{dx}(12x^{2}-2x^{3})
inverse oflaplace ((s+3))/((s-2)^2)	inverselaplace\:\frac{(s+3)}{(s-2)^{2}}
limit as x approaches 6 of sqrt(x)	\lim\:_{x\to\:6}(\sqrt{x})
area f(x)=x^3-x,[0,3]	area\:f(x)=x^{3}-x,[0,3]
integral of sin(x-2nx)	\int\:\sin(x-2nx)dx
derivative of x^5y^2	\frac{d}{dx}(x^{5}y^{2})
integral of 1/((x-1)^{3/2)}	\int\:\frac{1}{(x-1)^{\frac{3}{2}}}dx
integral from 0 to 4 of 1/((6-2x)^{1/3)}	\int\:_{0}^{4}\frac{1}{(6-2x)^{\frac{1}{3}}}dx
((y^'-e^{-t}+5)/y)=-5,y(0)=-2	(\frac{y^{\prime\:}-e^{-t}+5}{y})=-5,y(0)=-2
integral of 5/(sqrt(9-(x-3)^2))	\int\:\frac{5}{\sqrt{9-(x-3)^{2}}}dx
tangent of y= 2/(x-4)	tangent\:y=\frac{2}{x-4}
integral of 1/(k-x)	\int\:\frac{1}{k-x}dx
derivative of 9e^x+2/(\sqrt[3]{x)}	derivative\:9e^{x}+\frac{2}{\sqrt[3]{x}}
integral of (x+21)/(x^2+28x+200)	\int\:\frac{x+21}{x^{2}+28x+200}dx
integral of 4^x+ln(5^x)	\int\:4^{x}+\ln(5^{x})dx
inverse oflaplace 3/(s^2+7)	inverselaplace\:\frac{3}{s^{2}+7}
integral of 8x	\int\:8xdx
tangent of y=16sqrt(x),(16,64)	tangent\:y=16\sqrt{x},(16,64)
derivative of arctan(3/(x+2))	\frac{d}{dx}(\arctan(\frac{3}{x+2}))
integral of (sin(x))/(2+cos(x))	\int\:\frac{\sin(x)}{2+\cos(x)}dx
tangent of f(x)=(x^2+15)(2x+18)	tangent\:f(x)=(x^{2}+15)(2x+18)
integral of (16)/(1+x^2)	\int\:\frac{16}{1+x^{2}}dx
(dy)/(dx)=2(1-y)	\frac{dy}{dx}=2(1-y)
(\partial)/(\partial y)((-1)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{-1}{x^{2}+y^{2}})
(\partial)/(\partial x)(e^{(4xy)})	\frac{\partial\:}{\partial\:x}(e^{(4xy)})
derivative of y=xlog_{e}(x)	derivative\:y=x\log_{e}(x)
(\partial)/(\partial x)(2xy^3)	\frac{\partial\:}{\partial\:x}(2xy^{3})
limit as x approaches 4 of-2x^2+4x-4	\lim\:_{x\to\:4}(-2x^{2}+4x-4)

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