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Popular Calculus Problems

integral of 1/(9-6x)	\int\:\frac{1}{9-6x}dx
integral of 1/(e^x-1)	\int\:\frac{1}{e^{x}-1}dx
integral of sin(x/2)	\int\:\sin(\frac{x}{2})dx
derivative of f(x)= 1/(cos(x))	derivative\:f(x)=\frac{1}{\cos(x)}
d/(dy)(2xy^4e^y+2xy^3+y)	\frac{d}{dy}(2xy^{4}e^{y}+2xy^{3}+y)
y^{''}+4y^'+6y=cos(x),y(0)=0,y^'(0)=2	y^{\prime\:\prime\:}+4y^{\prime\:}+6y=\cos(x),y(0)=0,y^{\prime\:}(0)=2
sum from n=1 to infinity of (x^n)/(2n-1)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{2n-1}
(\partial)/(\partial x)(e^{xz})	\frac{\partial\:}{\partial\:x}(e^{xz})
limit as x approaches 0+of (1-4x)^{1/x}	\lim\:_{x\to\:0+}((1-4x)^{\frac{1}{x}})
integral of 6x(3x^2+4)^4	\int\:6x(3x^{2}+4)^{4}dx
derivative of ((x-2^3)/(x^2))	\frac{d}{dx}(\frac{(x-2)^{3}}{x^{2}})
derivative of sqrt(3x)+\sqrt[3]{x}+1/x	\frac{d}{dx}(\sqrt{3x}+\sqrt[3]{x}+\frac{1}{x})
(\partial)/(\partial x)(x^3+y^3-3xy)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{3}-3xy)
tangent of f(x)=7e^xcos(x),\at x=0	tangent\:f(x)=7e^{x}\cos(x),\at\:x=0
limit as x approaches 0 of ((x-4)/(x+1))^{x-2}	\lim\:_{x\to\:0}((\frac{x-4}{x+1})^{x-2})
derivative of (sqrt(x)x/(x^2))	\frac{d}{dx}(\frac{\sqrt{x}x}{x^{2}})
y^'+3y=e^{-4t},y(0)=5	y^{\prime\:}+3y=e^{-4t},y(0)=5
derivative of 9/(e^x-e^{-x})	\frac{d}{dx}(\frac{9}{e^{x}-e^{-x}})
x^2+3y(dy)/(dx)=0	x^{2}+3y\frac{dy}{dx}=0
integral from 0 to 16 of 1/(sqrt(x))	\int\:_{0}^{16}\frac{1}{\sqrt{x}}dx
y^'=ry	y^{\prime\:}=ry
y^{''}=-2/(t^2)	y^{\prime\:\prime\:}=-\frac{2}{t^{2}}
tangent of y=x^2+5x+9,\at x=4	tangent\:y=x^{2}+5x+9,\at\:x=4
(\partial)/(\partial x)(yze^{xz}+e^{xz}+xye^{xz})	\frac{\partial\:}{\partial\:x}(yze^{xz}+e^{xz}+xye^{xz})
area y=1.2(x+0.1)^{0.5}+4,1,-0.1	area\:y=1.2(x+0.1)^{0.5}+4,1,-0.1
sum from n=0 to infinity of 2^n2^n	\sum\:_{n=0}^{\infty\:}2^{n}2^{n}
(\partial)/(\partial z)(x^2y^2z^2)	\frac{\partial\:}{\partial\:z}(x^{2}y^{2}z^{2})
tangent of x^2-3x+6,\at x=1	tangent\:x^{2}-3x+6,\at\:x=1
derivative of 7x^2-3/x+2sqrt(x)	\frac{d}{dx}(7x^{2}-\frac{3}{x}+2\sqrt{x})
derivative of (sqrt(x-3)/(sqrt(x+3)))	\frac{d}{dx}(\frac{\sqrt{x-3}}{\sqrt{x+3}})
derivative of sqrt(x^2+7)	derivative\:\sqrt{x^{2}+7}
integral of x^2sqrt(2x-1)	\int\:x^{2}\sqrt{2x-1}dx
(dx)/(dt)+t^7x^9+x/t =0	\frac{dx}{dt}+t^{7}x^{9}+\frac{x}{t}=0
(d^2)/(dx^2)(cos(sin(3θ)))	\frac{d^{2}}{dx^{2}}(\cos(\sin(3θ)))
tangent of f(x)=-(24)/((4x+1)),\at x=-1	tangent\:f(x)=-\frac{24}{(4x+1)},\at\:x=-1
derivative of (6e^w)/(7w)	derivative\:\frac{6e^{w}}{7w}
derivative of 14^{2x}	\frac{d}{dx}(14^{2x})
derivative of (5u)/(4u^2+1)	derivative\:\frac{5u}{4u^{2}+1}
tangent of f(x)=sqrt(x+2),\at x=2	tangent\:f(x)=\sqrt{x+2},\at\:x=2
taylor \sqrt[3]{1+x},0	taylor\:\sqrt[3]{1+x},0
tangent of x^3+x^2+6/x	tangent\:x^{3}+x^{2}+\frac{6}{x}
integral of (8x)/(x^2-3)	\int\:\frac{8x}{x^{2}-3}dx
integral of 1/(sin^2(2x)cos^2(2x))	\int\:\frac{1}{\sin^{2}(2x)\cos^{2}(2x)}dx
integral of sec^3(x)-sec(x)	\int\:\sec^{3}(x)-\sec(x)dx
integral from 0 to 1 of ((9t)/(1+t^2))	\int\:_{0}^{1}(\frac{9t}{1+t^{2}})dt
y^'=x(3-y)	y^{\prime\:}=x(3-y)
integral of (x^3(x^2-2x)^3)	\int\:(x^{3}(x^{2}-2x)^{3})dx
derivative of y= 1/2 (e^x-e^{-x})	derivative\:y=\frac{1}{2}(e^{x}-e^{-x})
derivative of 925+20x-0.079x^2	derivative\:925+20x-0.079x^{2}
integral from-9 to 0 of 1/(sqrt(16-x))	\int\:_{-9}^{0}\frac{1}{\sqrt{16-x}}dx
derivative of ln(5x^3+2x)	\frac{d}{dx}(\ln(5x^{3}+2x))
integral of x^2-x	\int\:x^{2}-xdx
derivative of \|x-4\|	\frac{d}{dx}(\left\|x-4\right\|)
derivative of sin^3(x^2-1)	\frac{d}{dx}(\sin^{3}(x^{2}-1))
integral of (x+arctan(x))/(1+x^2)	\int\:\frac{x+\arctan(x)}{1+x^{2}}dx
derivative of x^{arcsin(x})	\frac{d}{dx}(x^{\arcsin(x)})
derivative of (4x+4sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{4x+4\sqrt{1+x}}{x^{2}-1})
integral of (8x^2+10)/(x^3+5x)	\int\:\frac{8x^{2}+10}{x^{3}+5x}dx
x^3=(2sqrt(y^5+4))/(5y^4y^')	x^{3}=\frac{2\sqrt{y^{5}+4}}{5y^{4}y^{\prime\:}}
integral of sin(16x)cos(7x)	\int\:\sin(16x)\cos(7x)dx
(\partial)/(\partial x)(x^7y^6)	\frac{\partial\:}{\partial\:x}(x^{7}y^{6})
integral of sqrt(5x-1)	\int\:\sqrt{5x-1}dx
(dy)/(dx)=8-y/(50),y(0)=50	\frac{dy}{dx}=8-\frac{y}{50},y(0)=50
y^{''}=6t	y^{\prime\:\prime\:}=6t
derivative of f(x)= 1/(x^8)	derivative\:f(x)=\frac{1}{x^{8}}
derivative of sqrt(x)+1/x	\frac{d}{dx}(\sqrt{x}+\frac{1}{x})
integral of 2x+5	\int\:2x+5dx
tangent of f(x)=-2x^4,\at x=3	tangent\:f(x)=-2x^{4},\at\:x=3
d/(d{r)}(-arctan({r})+2arccot({r})-ln({r}))	\frac{d}{d{r}}(-\arctan({r})+2\arccot({r})-\ln({r}))
integral of 19	\int\:19dx
(\partial)/(\partial x)(2x+5y)	\frac{\partial\:}{\partial\:x}(2x+5y)
integral of 13cos(pix)cos(4pix)	\int\:13\cos(πx)\cos(4πx)dx
sum from n=0 to infinity of cos(7pin)	\sum\:_{n=0}^{\infty\:}\cos(7πn)
integral of sqrt(t)(t^2-3t+5)	\int\:\sqrt{t}(t^{2}-3t+5)dt
tangent of f(x)= 3/(x+1),\at x=2	tangent\:f(x)=\frac{3}{x+1},\at\:x=2
integral of sin^2(θ)cos^5(θ)	\int\:\sin^{2}(θ)\cos^{5}(θ)dθ
(\partial)/(\partial x)(e^{5xy})	\frac{\partial\:}{\partial\:x}(e^{5xy})
integral of (sqrt(x))/(\sqrt[3]{x)}	\int\:\frac{\sqrt{x}}{\sqrt[3]{x}}dx
derivative of sec^2(xtan^2(x))	\frac{d}{dx}(\sec^{2}(x)\tan^{2}(x))
integral of (2x+4)/(x^2-x)	\int\:\frac{2x+4}{x^{2}-x}dx
(\partial)/(\partial x)(1/3 x^{3/2})	\frac{\partial\:}{\partial\:x}(\frac{1}{3}x^{\frac{3}{2}})
(\partial)/(\partial y)(6xcos(x)cos(y))	\frac{\partial\:}{\partial\:y}(6x\cos(x)\cos(y))
y^'+y=-x	y^{\prime\:}+y=-x
limit as x approaches 0 of (((6+x)^{-1}-6^{-1}))/x	\lim\:_{x\to\:0}(\frac{((6+x)^{-1}-6^{-1})}{x})
derivative of f(x)=(x^2-6x+12)/(x-4)	derivative\:f(x)=\frac{x^{2}-6x+12}{x-4}
slope of x^2-3x	slope\:x^{2}-3x
integral from 0 to 3 of 1/(x^4)	\int\:_{0}^{3}\frac{1}{x^{4}}dx
integral of 18cot^4(x)	\int\:18\cot^{4}(x)dx
integral of sqrt(y^2-1)	\int\:\sqrt{y^{2}-1}dy
tangent of f(x)=x^3-2x+2,(4,58)	tangent\:f(x)=x^{3}-2x+2,(4,58)
laplacetransform e^{-t}(cos(4t)-2sin(4t))	laplacetransform\:e^{-t}(\cos(4t)-2\sin(4t))
d/(dt)(t^2e^t)	\frac{d}{dt}(t^{2}e^{t})
taylor 3/((x^2-x-2))	taylor\:\frac{3}{(x^{2}-x-2)}
derivative of (2+x^{1/3}(1-x)^{2/3})	\frac{d}{dx}((2+x)^{\frac{1}{3}}(1-x)^{\frac{2}{3}})
integral of 9/((x-1)(x+8))	\int\:\frac{9}{(x-1)(x+8)}dx
taylor 4x^4+3x^3+2x^2+x+1	taylor\:4x^{4}+3x^{3}+2x^{2}+x+1
d/(dt)(6ln(cos(t)))	\frac{d}{dt}(6\ln(\cos(t)))
integral of ((x+4))/(2x+3)	\int\:\frac{(x+4)}{2x+3}dx
integral of 5e^{-5x}	\int\:5e^{-5x}dx
derivative of arctan(1/(1+x^2))	\frac{d}{dx}(\arctan(\frac{1}{1+x^{2}}))

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