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Popular Calculus Problems

integral from 0 to 1 of 13 1/(x^p)	\int\:_{0}^{1}13\frac{1}{x^{p}}dx
(\partial)/(\partial x)(5xye^{-y^2})	\frac{\partial\:}{\partial\:x}(5xye^{-y^{2}})
integral of ((15)/(x^4)+8/(x^5))	\int\:(\frac{15}{x^{4}}+\frac{8}{x^{5}})dx
derivative of (sin(3x)/x)	\frac{d}{dx}(\frac{\sin(3x)}{x})
6y^{''}+8y^'+y=0,y(-2)=-3,y^'(-2)=-4	6y^{\prime\:\prime\:}+8y^{\prime\:}+y=0,y(-2)=-3,y^{\prime\:}(-2)=-4
integral of (7x+1)/(6x^2+x-1)	\int\:\frac{7x+1}{6x^{2}+x-1}dx
limit as x approaches 4 of-(15)/(x-4)	\lim\:_{x\to\:4}(-\frac{15}{x-4})
(\partial)/(\partial x)(sin(pix))	\frac{\partial\:}{\partial\:x}(\sin(πx))
derivative of 4x^5	\frac{d}{dx}(4x^{5})
y^{''}-3y^'+2y=e^{5x}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{5x}
derivative of cos(x+sin(x))	\frac{d}{dx}(\cos(x)+\sin(x))
slope ofintercept (9,-5),(6,4)	slopeintercept\:(9,-5),(6,4)
slope of f(x)=(1+3x^{1/2})/(5+x^{3/2)}	slope\:f(x)=\frac{1+3x^{\frac{1}{2}}}{5+x^{\frac{3}{2}}}
derivative of y=7x+4	derivative\:y=7x+4
derivative of 6x^2cos(x)cot(x)	derivative\:6x^{2}\cos(x)\cot(x)
integral from 1 to 3 of x^3+2x-3	\int\:_{1}^{3}x^{3}+2x-3dx
derivative of f(x)=(3x+5)^2	derivative\:f(x)=(3x+5)^{2}
integral of 1/(cos(x)+1)	\int\:\frac{1}{\cos(x)+1}dx
derivative of f(x)=3x^2+2x+1	derivative\:f(x)=3x^{2}+2x+1
area x^2-4x+7,2x^2-3x+1	area\:x^{2}-4x+7,2x^{2}-3x+1
derivative of y=4x^2-5x	derivative\:y=4x^{2}-5x
derivative of xsin(5x)	derivative\:x\sin(5x)
tangent of-2sin(x),\at x=-pi/3	tangent\:-2\sin(x),\at\:x=-\frac{π}{3}
integral from 3 to 0 of x^2	\int\:_{3}^{0}x^{2}dx
tangent of (5x)/(x+2)	tangent\:\frac{5x}{x+2}
integral of (sin(x))^6	\int\:(\sin(x))^{6}dx
(\partial)/(\partial x)(ze^x)	\frac{\partial\:}{\partial\:x}(ze^{x})
integral of 4e^x+cos(x/2)	\int\:4e^{x}+\cos(\frac{x}{2})dx
derivative of (-25x^2+1^2)	\frac{d}{dx}((-25x^{2}+1)^{2})
(\partial)/(\partial x)(-(7x^2)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(-\frac{7x^{2}}{(x-y)^{2}})
derivative of ax^{b^2-c}	\frac{d}{dx}(ax^{b^{2}-c})
(\partial)/(\partial x)(xy+2z)	\frac{\partial\:}{\partial\:x}(xy+2z)
derivative of f(x)=x^{-1/5}+x^{1/5}	derivative\:f(x)=x^{-\frac{1}{5}}+x^{\frac{1}{5}}
limit as x approaches 1-of G(x)	\lim\:_{x\to\:1-}(G(x))
limit as x approaches-infinity of-5^x	\lim\:_{x\to\:-\infty\:}(-5^{x})
limit as x approaches 0 of (x^3)/(x^2+x)	\lim\:_{x\to\:0}(\frac{x^{3}}{x^{2}+x})
xy^'+y=-9xy^2	xy^{\prime\:}+y=-9xy^{2}
integral of 6x(x^2+9)^5	\int\:6x(x^{2}+9)^{5}dx
(19y^2-xy)dx+x^2dy=0	(19y^{2}-xy)dx+x^{2}dy=0
integral of cos(pi)t	\int\:\cos(π)tdt
(\partial)/(\partial x)(a^3-a+x)	\frac{\partial\:}{\partial\:x}(a^{3}-a+x)
derivative of sin(cos^2(x))	\frac{d}{dx}(\sin(\cos^{2}(x)))
sum from n=0 to infinity of (4/9)^n	\sum\:_{n=0}^{\infty\:}(\frac{4}{9})^{n}
area x^2-8,1	area\:x^{2}-8,1
(dy)/(dx)=sqrt(y)	\frac{dy}{dx}=\sqrt{y}
y^{''}+y+x=0,y(0)=0,y^'(1)=0	y^{\prime\:\prime\:}+y+x=0,y(0)=0,y^{\prime\:}(1)=0
inverse oflaplace (s+2)/(s^2+4s+6)	inverselaplace\:\frac{s+2}{s^{2}+4s+6}
derivative of (2/5 ^{sqrt(x)})	\frac{d}{dx}((\frac{2}{5})^{\sqrt{x}})
integral of (1+x)(2x+x^2)^5	\int\:(1+x)(2x+x^{2})^{5}dx
derivative of (x-4(2x+x^2))	\frac{d}{dx}((x-4)(2x+x^{2}))
derivative of f(x)=3t^3-18t^2+2	derivative\:f(x)=3t^{3}-18t^{2}+2
derivative of 2x^{5/3}-5x^{4/3}	\frac{d}{dx}(2x^{\frac{5}{3}}-5x^{\frac{4}{3}})
limit as x approaches-infinity of-x	\lim\:_{x\to\:-\infty\:}(-x)
integral of 8x(4x^2+4)^4	\int\:8x(4x^{2}+4)^{4}dx
derivative of (2x^4+5)/(x^2)	derivative\:\frac{2x^{4}+5}{x^{2}}
integral of 6cos(x)-9/(sqrt(1-x^2))	\int\:6\cos(x)-\frac{9}{\sqrt{1-x^{2}}}dx
integral of-2e^{-1/2 x}	\int\:-2e^{-\frac{1}{2}x}dx
laplacetransform 3sin(5t+45)	laplacetransform\:3\sin(5t+45^{\circ\:})
x^2-2y^2+2xyy^'=0	x^{2}-2y^{2}+2xyy^{\prime\:}=0
derivative of 1/(sqrt(4-x))	\frac{d}{dx}(\frac{1}{\sqrt{4-x}})
integral of 1/(3x-7)	\int\:\frac{1}{3x-7}dx
laplacetransform e^{(3t)}	laplacetransform\:e^{(3t)}
(dy)/(dx)=(2x+sec^2(x))/(2y),y(0)=-3	\frac{dy}{dx}=\frac{2x+\sec^{2}(x)}{2y},y(0)=-3
derivative of-3+8x	\frac{d}{dx}(-3+8x)
integral from 1 to 2 of (y^4)/8+1/(4y^2)	\int\:_{1}^{2}\frac{y^{4}}{8}+\frac{1}{4y^{2}}dy
derivative of-sin(pix)	\frac{d}{dx}(-\sin(πx))
integral of 1/((x-1)(1-2x))	\int\:\frac{1}{(x-1)(1-2x)}dx
derivative of cos({f}(x))	\frac{d}{dx}(\cos({f}(x)))
2y(dy)/(dx)-xy^2=x	2y\frac{dy}{dx}-xy^{2}=x
derivative of arcsin(x-2x)	\frac{d}{dx}(\arcsin(x)-2x)
derivative of ((5x^2+9)^5)/((x-3)^4)	derivative\:\frac{(5x^{2}+9)^{5}}{(x-3)^{4}}
integral of xy^3	\int\:xy^{3}dx
integral of x^3tan^3(x^4)	\int\:x^{3}\tan^{3}(x^{4})dx
f(x)=3sqrt(x)	f(x)=3\sqrt{x}
y^'+1/(x+8)y=x^{-2},y(1)=5	y^{\prime\:}+\frac{1}{x+8}y=x^{-2},y(1)=5
derivative of ((x+1^3)/(x^{3/2)})	\frac{d}{dx}(\frac{(x+1)^{3}}{x^{\frac{3}{2}}})
inverse oflaplace (5+5s)/((s^2+25)^2)	inverselaplace\:\frac{5+5s}{(s^{2}+25)^{2}}
tangent of f(x)=4x-x^2,\at x=1	tangent\:f(x)=4x-x^{2},\at\:x=1
limit as x approaches-2-of (x^2-4)/(x+2)	\lim\:_{x\to\:-2-}(\frac{x^{2}-4}{x+2})
integral of xsqrt(x^2-2)	\int\:x\sqrt{x^{2}-2}dx
limit as x approaches 0 of pi/x	\lim\:_{x\to\:0}(\frac{π}{x})
tangent of f(x)=xsqrt(x^2+21)	tangent\:f(x)=x\sqrt{x^{2}+21}
integral from-e to 0 of e^{2x}	\int\:_{-e}^{0}e^{2x}dx
integral of 3(sqrt(x)ln(x))	\int\:3(\sqrt{x}\ln(x))dx
integral of sin^3(x/2)cos^5(x/2)	\int\:\sin^{3}(\frac{x}{2})\cos^{5}(\frac{x}{2})dx
limit as x approaches-infinity of (x^2)/(4-x^2)	\lim\:_{x\to\:-\infty\:}(\frac{x^{2}}{4-x^{2}})
integral of 1/(2+y^2)	\int\:\frac{1}{2+y^{2}}dy
derivative of cot^6(x)	derivative\:\cot^{6}(x)
y^{''}+25y=tsin(2t)	y^{\prime\:\prime\:}+25y=t\sin(2t)
derivative of 0.5e^{-0.5(x-1})	\frac{d}{dx}(0.5e^{-0.5(x-1)})
81y^{''}+144y^'+64y=0	81y^{\prime\:\prime\:}+144y^{\prime\:}+64y=0
(\partial)/(\partial x)(1/(2cos^2(x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{2\cos^{2}(x)})
limit as x approaches infinity of arcsec(x)	\lim\:_{x\to\:\infty\:}(\arcsec(x))
integral of 3x^2+x	\int\:3x^{2}+xdx
limit as x approaches 10-of 1/((x-10)^2)	\lim\:_{x\to\:10-}(\frac{1}{(x-10)^{2}})
derivative of f(x)=e^θsin(6θ)	derivative\:f(x)=e^{θ}\sin(6θ)
limit as x approaches 2 of 3x^2-x+5	\lim\:_{x\to\:2}(3x^{2}-x+5)
(\partial)/(\partial x)(-5x^2-5y^2+xy)	\frac{\partial\:}{\partial\:x}(-5x^{2}-5y^{2}+xy)
yy^'=3((y^2-2)/(x^3))x^2	yy^{\prime\:}=3(\frac{y^{2}-2}{x^{3}})x^{2}
derivative of ((x+9/(x-9))^5)	\frac{d}{dx}((\frac{x+9}{x-9})^{5})

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