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Popular Calculus Problems

integral from-3 to 3 of (9-x^2)^2	\int\:_{-3}^{3}(9-x^{2})^{2}dx
integral of (1-x^2)/(x(x^2+1))	\int\:\frac{1-x^{2}}{x(x^{2}+1)}dx
integral of e^x+x^2	\int\:e^{x}+x^{2}dx
limit as x approaches 0 of 0	\lim\:_{x\to\:0}(0)
derivative of 3x^7	\frac{d}{dx}(3x^{7})
integral from 4 to infinity of xe^{-x}	\int\:_{4}^{\infty\:}xe^{-x}dx
derivative of f(r)=sqrt(r)+\sqrt[7]{r}	derivative\:f(r)=\sqrt{r}+\sqrt[7]{r}
integral of (2xe^{-3x})	\int\:(2xe^{-3x})dx
limit as x approaches 0 of (3tan(x))/x	\lim\:_{x\to\:0}(\frac{3\tan(x)}{x})
y^'+2sin(2x)y=2sin(2x),y(pi/2)=3	y^{\prime\:}+2\sin(2x)y=2\sin(2x),y(\frac{π}{2})=3
(dx)/(dy)=xy	\frac{dx}{dy}=xy
derivative of-csc(x-sin(x))	\frac{d}{dx}(-\csc(x)-\sin(x))
integral of 5sin^3(9x)	\int\:5\sin^{3}(9x)dx
(\partial)/(\partial y)(4xy-2e^{2x+y})	\frac{\partial\:}{\partial\:y}(4xy-2e^{2x+y})
limit as h approaches 0 of (-4)^2+2(-4)	\lim\:_{h\to\:0}((-4)^{2}+2(-4))
integral of (x^2)/(sqrt(21+4x-x^2))	\int\:\frac{x^{2}}{\sqrt{21+4x-x^{2}}}dx
inverse oflaplace ((s+9))/((s^2+6s+34))	inverselaplace\:\frac{(s+9)}{(s^{2}+6s+34)}
integral of x^2sqrt(x^3+19)	\int\:x^{2}\sqrt{x^{3}+19}dx
(dy)/(dx)-2/x y= 3/(x^2)y^4	\frac{dy}{dx}-\frac{2}{x}y=\frac{3}{x^{2}}y^{4}
integral from 1 to 2 of 13sqrt(4x^2-3)	\int\:_{1}^{2}13\sqrt{4x^{2}-3}dx
derivative of-5x+2	\frac{d}{dx}(-5x+2)
(\partial)/(\partial y)(2x-y^2)	\frac{\partial\:}{\partial\:y}(2x-y^{2})
derivative of-5/(4y^3)	derivative\:-\frac{5}{4y^{3}}
derivative of cos(x^{-5})	\frac{d}{dx}(\cos(x^{-5}))
integral of (2sin(θ)-csc(θ))^2	\int\:(2\sin(θ)-\csc(θ))^{2}dθ
derivative of y=(4x-5)2	derivative\:y=(4x-5)2
(x+9/x)^'	(x+\frac{9}{x})^{\prime\:}
integral of 7cot^4(5t)	\int\:7\cot^{4}(5t)dt
integral from-1 to 1 of 1-x^4	\int\:_{-1}^{1}1-x^{4}dx
(\partial)/(\partial y)(y(-2x-y+1))	\frac{\partial\:}{\partial\:y}(y(-2x-y+1))
integral from pi/2 to pi of-cos(x)	\int\:_{\frac{π}{2}}^{π}-\cos(x)dx
integral of x^2e^{-x}	\int\:x^{2}e^{-x}dx
derivative of h(t)=3ln(t^6)	derivative\:h(t)=3\ln(t^{6})
integral of 24+cos(x)	\int\:24+\cos(x)dx
tangent of (-4x)/(x^2+1)(-1.2)	tangent\:\frac{-4x}{x^{2}+1}(-1.2)
d/(d{x)}({x}^2+{x}{z}-{y}+{y}^2+{y}{z}+3{z}^2)	\frac{d}{d{x}}({x}^{2}+{x}{z}-{y}+{y}^{2}+{y}{z}+3{z}^{2})
integral of x*e^{x/4}	\int\:x\cdot\:e^{\frac{x}{4}}dx
(\partial)/(\partial x)(4sqrt(y/x))	\frac{\partial\:}{\partial\:x}(4\sqrt{\frac{y}{x}})
d/(dy)(xy)	\frac{d}{dy}(xy)
derivative of y=(x)	derivative\:y=(x)
area y=4x-16,y^2=4x+4	area\:y=4x-16,y^{2}=4x+4
derivative of y=arctan(sqrt(7x^2-1))	derivative\:y=\arctan(\sqrt{7x^{2}-1})
integral of x(cos^2(x))	\int\:x(\cos^{2}(x))dx
derivative of y=x^2-2x-8	derivative\:y=x^{2}-2x-8
integral of (x^2+y)	\int\:(x^{2}+y)dx
d/(dy)(1/(sqrt(y^2+1)))	\frac{d}{dy}(\frac{1}{\sqrt{y^{2}+1}})
y^'+2xy=2x^3	y^{\prime\:}+2xy=2x^{3}
derivative of (x^2-3/(x+2))	\frac{d}{dx}(\frac{x^{2}-3}{x+2})
integral from 0 to 4 of 4x	\int\:_{0}^{4}4xdx
integral of (sin(x))/((1+cos(x))^3)	\int\:\frac{\sin(x)}{(1+\cos(x))^{3}}dx
x^{''}=0	x^{\prime\:\prime\:}=0
integral of cos^5(x)sqrt(sin(x))	\int\:\cos^{5}(x)\sqrt{\sin(x)}dx
derivative of xln(x+2)	\frac{d}{dx}(x\ln(x+2))
y^{''}+16y=1+2sin(4x)	y^{\prime\:\prime\:}+16y=1+2\sin(4x)
tangent of (3x)/(4-x^2),\at x=1	tangent\:\frac{3x}{4-x^{2}},\at\:x=1
integral from b to 1 of 2ln(x)	\int\:_{b}^{1}2\ln(x)dx
integral of (x^2+2)^{3/2}	\int\:(x^{2}+2)^{\frac{3}{2}}dx
derivative of (x-sqrt(x)/(x^{1/5)})	\frac{d}{dx}(\frac{x-\sqrt{x}}{x^{\frac{1}{5}}})
integral of (x^3)/(sqrt((4-x^2)^3))	\int\:\frac{x^{3}}{\sqrt{(4-x^{2})^{3}}}dx
y^'=(x+y-1)^2-1	y^{\prime\:}=(x+y-1)^{2}-1
(\partial)/(\partial x)(t/(x-1))	\frac{\partial\:}{\partial\:x}(\frac{t}{x-1})
integral of 2x-2y	\int\:2x-2ydx
taylor 1/(1-z^2),0	taylor\:\frac{1}{1-z^{2}},0
(\partial)/(\partial x)(1/2 ln(x))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}\ln(x))
(x^2+1)y^'+8x(y-1)=0,y(0)=3	(x^{2}+1)y^{\prime\:}+8x(y-1)=0,y(0)=3
(\partial)/(\partial x)(4x^2-4xy+xyz)	\frac{\partial\:}{\partial\:x}(4x^{2}-4xy+xyz)
integral of (tan(x))/(1+cos(x))	\int\:\frac{\tan(x)}{1+\cos(x)}dx
area 6-x^2,x^2-2,[0,3]	area\:6-x^{2},x^{2}-2,[0,3]
integral of (ln(y))/(ln(y))	\int\:\frac{\ln(y)}{\ln(y)}dy
e^{t^2}y^'+(t+ty^2)=0,y(0)=1	e^{t^{2}}y^{\prime\:}+(t+ty^{2})=0,y(0)=1
tangent of (64x)/(x^2+64)	tangent\:\frac{64x}{x^{2}+64}
(\partial)/(\partial y)(2x^3-x^2y)	\frac{\partial\:}{\partial\:y}(2x^{3}-x^{2}y)
integral of (t^2-1)(4+3t)	\int\:(t^{2}-1)(4+3t)dt
tangent of f(x)=x^4,\at x=1	tangent\:f(x)=x^{4},\at\:x=1
tangent of y= 6/(sqrt(x)),(25, 6/5)	tangent\:y=\frac{6}{\sqrt{x}},(25,\frac{6}{5})
derivative of (x^2)/(7+sqrt(x))	derivative\:\frac{x^{2}}{7+\sqrt{x}}
limit as x approaches infinity of ((sqrt(2x^2+1)))/(3x-5)	\lim\:_{x\to\:\infty\:}(\frac{(\sqrt{2x^{2}+1})}{3x-5})
y^{''}-2y^'=2t	y^{\prime\:\prime\:}-2y^{\prime\:}=2t
limit as x approaches 3+of (x^2+x)/(x-3)	\lim\:_{x\to\:3+}(\frac{x^{2}+x}{x-3})
laplacetransform cos(t+pi/4)	laplacetransform\:\cos(t+\frac{π}{4})
integral of (3y+7)	\int\:(3y+7)dy
inverse oflaplace 5/(s+2)	inverselaplace\:\frac{5}{s+2}
derivative of x^{2x}	derivative\:x^{2x}
x^2(dy)/(dx)-2xy=4y^4,y(1)= 1/3	x^{2}\frac{dy}{dx}-2xy=4y^{4},y(1)=\frac{1}{3}
xy^'+y^2+y=0	xy^{\prime\:}+y^{2}+y=0
derivative of f(x)=3x^2+2x	derivative\:f(x)=3x^{2}+2x
derivative of f(x)=sin^2(x)+cos^2(x)	derivative\:f(x)=\sin^{2}(x)+\cos^{2}(x)
integral from 1 to 2 of 2x	\int\:_{1}^{2}2xdx
d/(dt)(st^2)	\frac{d}{dt}(st^{2})
tangent of-4x^2-3x+2,\at x=-1	tangent\:-4x^{2}-3x+2,\at\:x=-1
integral of 1/(5x^4)	\int\:\frac{1}{5x^{4}}dx
derivative of (sin(x)/(sqrt(1+cos(x))))	\frac{d}{dx}(\frac{\sin(x)}{\sqrt{1+\cos(x)}})
integral of 22x	\int\:22xdx
(dx)/(dt)=(e^t-e^{-t})/(3+x)	\frac{dx}{dt}=\frac{e^{t}-e^{-t}}{3+x}
derivative of y= 1/2 e^{2x}	derivative\:y=\frac{1}{2}e^{2x}
(\partial)/(\partial x)(2xyz+3/4 xy+z)	\frac{\partial\:}{\partial\:x}(2xyz+\frac{3}{4}xy+z)
(dy)/(dt)+0.4ty=5t,y(0)=6	\frac{dy}{dt}+0.4ty=5t,y(0)=6
tangent of y=x^3-11x,(2,-14)	tangent\:y=x^{3}-11x,(2,-14)
(\partial)/(\partial x)(arctan(a)x^3)	\frac{\partial\:}{\partial\:x}(\arctan(a)x^{3})
integral of (-t)/((t+1)-sqrt(t+1))	\int\:\frac{-t}{(t+1)-\sqrt{t+1}}dt

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