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Popular Calculus Problems

integral from-5 to 5 of 4(25-x^2)	\int\:_{-5}^{5}4(25-x^{2})dx
derivative of sqrt(8x-5)	derivative\:\sqrt{8x-5}
(d^4)/(dx^4)(ln(1+x))	\frac{d^{4}}{dx^{4}}(\ln(1+x))
y^'+x=0	y^{\prime\:}+x=0
integral of sqrt(8-4x-4x^2)	\int\:\sqrt{8-4x-4x^{2}}dx
limit as x approaches 0 of x^2+4x+2	\lim\:_{x\to\:0}(x^{2}+4x+2)
sum from n=1 to infinity of 1/(ln(n+1))	\sum\:_{n=1}^{\infty\:}\frac{1}{\ln(n+1)}
y^'=k(y-9-10cos(2pit))	y^{\prime\:}=k(y-9-10\cos(2\cdot\:π\cdot\:t))
(d^2)/(dx^2)(2sin(-4x-3))	\frac{d^{2}}{dx^{2}}(2\sin(-4x-3))
sum from n=2 to infinity of 1/(5^n)	\sum\:_{n=2}^{\infty\:}\frac{1}{5^{n}}
limit as x approaches 0 of (sin(x))/(8x)	\lim\:_{x\to\:0}(\frac{\sin(x)}{8x})
f(x)=(sin(x)+cos(x))/(e^x)	f(x)=\frac{\sin(x)+\cos(x)}{e^{x}}
integral of 3x^2-8x+C	\int\:3x^{2}-8x+Cdx
derivative of h(x)=(xtan(x))^7	derivative\:h(x)=(x\tan(x))^{7}
integral of xsin(ax)	\int\:x\sin(ax)dx
integral of ln(cos(x))	\int\:\ln(\cos(x))dx
y^'=1-y/(100)	y^{\prime\:}=1-\frac{y}{100}
tangent of sin(x)	tangent\:\sin(x)
derivative of 5(x^{2n-1})*(2x^{3n+1})^2	derivative\:5(x^{2n-1})\cdot\:(2x^{3n+1})^{2}
f(x)=xe^{1/x}	f(x)=xe^{\frac{1}{x}}
limit as x approaches 0 of (e^{-1x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{-1x}-1}{x})
integral of sin(x)ln(c)osx	\int\:\sin(x)\ln(c)osxdx
laplacetransform sin(2t)sin(5t)	laplacetransform\:\sin(2t)\sin(5t)
(\partial)/(\partial x)(yx+2x)	\frac{\partial\:}{\partial\:x}(yx+2x)
integral of (1+sin(x))/(1-sin(x))	\int\:\frac{1+\sin(x)}{1-\sin(x)}dx
integral of xln(x+2)	\int\:x\ln(x+2)dx
integral from 0 to 1 of 2pixe^{-x^2}	\int\:_{0}^{1}2πxe^{-x^{2}}dx
derivative of xy^'-y	\frac{d}{dx}(xy^{\prime\:}-y)
integral of 1/(x^2+x-6)	\int\:\frac{1}{x^{2}+x-6}dx
tangent of 9x^2	tangent\:9x^{2}
derivative of ln(x^2-5x+2)	\frac{d}{dx}(\ln(x^{2}-5x+2))
integral of (ln(2))/(x^2)	\int\:\frac{\ln(2)}{x^{2}}dx
y^'=((3t^2-e^t))/((2y-5)),y(0)=1	y^{\prime\:}=\frac{(3t^{2}-e^{t})}{(2y-5)},y(0)=1
sum from n=1 to infinity of ln(n+2)	\sum\:_{n=1}^{\infty\:}\ln(n+2)
limit as x approaches 2-of ln(x^2(3-x))	\lim\:_{x\to\:2-}(\ln(x^{2}(3-x)))
area x^2,2-x^2	area\:x^{2},2-x^{2}
limit as x approaches 0 of 1/2	\lim\:_{x\to\:0}(\frac{1}{2})
integral from 0 to 1 of x(1-x)^8	\int\:_{0}^{1}x(1-x)^{8}dx
area f(x)=sin(x),0, pi/2	area\:f(x)=\sin(x),0,\frac{π}{2}
derivative of xe^{5y}	\frac{d}{dx}(xe^{5y})
tangent of y=(4x)/(x+3),(1,1)	tangent\:y=\frac{4x}{x+3},(1,1)
integral of x^2e^{x^{3+4}}	\int\:x^{2}e^{x^{3+4}}dx
tangent of f(x)=log_{2}(2x^2+14),\at x=5	tangent\:f(x)=\log_{2}(2x^{2}+14),\at\:x=5
limit as x approaches 2 of 0/4	\lim\:_{x\to\:2}(\frac{0}{4})
taylor 1/(x-1),5	taylor\:\frac{1}{x-1},5
tangent of y=8x-x^2	tangent\:y=8x-x^{2}
integral of (x+4)^{1/2}	\int\:(x+4)^{\frac{1}{2}}dx
(dy)/(dx)=(sqrt(2x))	\frac{dy}{dx}=(\sqrt{2x})
limit as x approaches infinity of (4x^2)/(e^{4x)}	\lim\:_{x\to\:\infty\:}(\frac{4x^{2}}{e^{4x}})
(\partial)/(\partial x)(x^3+x^2*x^3-2y^2)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}\cdot\:x^{3}-2y^{2})
derivative of (x-2/(x^2+1))	\frac{d}{dx}(\frac{x-2}{x^{2}+1})
derivative of-16	\frac{d}{dx}(-16)
derivative of 5^{tan(5x})	\frac{d}{dx}(5^{\tan(5x)})
slope of (-5,3),(2,-3)	slope\:(-5,3),(2,-3)
(x^4(x-3)^3)^'	(x^{4}(x-3)^{3})^{\prime\:}
integral of-1/(y^2)	\int\:-\frac{1}{y^{2}}dy
derivative of cos(7x*7)	\frac{d}{dx}(\cos(7x)\cdot\:7)
integral of (10sin(5x))	\int\:(10\sin(5x))dx
derivative of 6*3^x	\frac{d}{dx}(6\cdot\:3^{x})
area y=2-x/2 ,x=2y^2	area\:y=2-\frac{x}{2},x=2y^{2}
integral of (9x+2)^2	\int\:(9x+2)^{2}dx
integral of (a+bx^5)/(6ax+bx^6)	\int\:\frac{a+bx^{5}}{6ax+bx^{6}}dx
y^{''}+4y^'-24y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-24y=0
integral of e^x+e^xx	\int\:e^{x}+e^{x}xdx
derivative of g(x)= 1/(sqrt(x))	derivative\:g(x)=\frac{1}{\sqrt{x}}
inverse oflaplace 6/s+(16)/(s^2+16)	inverselaplace\:\frac{6}{s}+\frac{16}{s^{2}+16}
(d^2y)/(dx^2)=0	\frac{d^{2}y}{dx^{2}}=0
integral from-1 to 1 of e^x-1	\int\:_{-1}^{1}e^{x}-1dx
limit as x approaches-1+of x^2-3	\lim\:_{x\to\:-1+}(x^{2}-3)
xydx+(1+y)sqrt(1)-x^2dy=0	xydx+(1+y)\sqrt{1}-x^{2}dy=0
integral of (6x)/(e^{3x^2)}	\int\:\frac{6x}{e^{3x^{2}}}dx
area (x^2)/4-1, x/4+4,[-4,5]	area\:\frac{x^{2}}{4}-1,\frac{x}{4}+4,[-4,5]
y^'+y-4sin(x)=0	y^{\prime\:}+y-4\sin(x)=0
integral of (9x+3)/(x^2+1)	\int\:\frac{9x+3}{x^{2}+1}dx
integral from x to 4 of 0.125	\int\:_{x}^{4}0.125dy
(\partial)/(\partial x)(rln(r^2+s))	\frac{\partial\:}{\partial\:x}(r\ln(r^{2}+s))
integral of sqrt(4x^2-4x+10)	\int\:\sqrt{4x^{2}-4x+10}dx
integral from 0 to 2 of f(x^3)	\int\:_{0}^{2}f(x^{3})dx
(d^2x)/(dx^2)	\frac{d^{2}x}{dx^{2}}
xy^'+2y=(3e^{-4x})/x	xy^{\prime\:}+2y=\frac{3e^{-4x}}{x}
limit as x approaches-1+of x/(x^2-1)	\lim\:_{x\to\:-1+}(\frac{x}{x^{2}-1})
integral from 0 to 4 of 5e^{-x^2}	\int\:_{0}^{4}5e^{-x^{2}}dx
parity (cot(x))/x	parity\:\frac{\cot(x)}{x}
limit as x approaches 0 of (20sin(x))/4	\lim\:_{x\to\:0}(\frac{20\sin(x)}{4})
limit as x approaches 0 of x(e^x-1)ln(x)	\lim\:_{x\to\:0}(x(e^{x}-1)\ln(x))
integral of sin((pix)/3)	\int\:\sin(\frac{πx}{3})dx
(x+y)^2dx+(2xy+x^2-7)dy=0	(x+y)^{2}dx+(2xy+x^{2}-7)dy=0
area 1-x^2,x^2-1	area\:1-x^{2},x^{2}-1
derivative of f(x)=2x^2+4x+3	derivative\:f(x)=2x^{2}+4x+3
(t^2+25)(dy)/(dt)+2ty=t^2(t^2+25)	(t^{2}+25)\frac{dy}{dt}+2ty=t^{2}(t^{2}+25)
inverse oflaplace ((2s+2.5))/((s+0.5))	inverselaplace\:\frac{(2s+2.5)}{(s+0.5)}
parity ln(csc(x)-cot(x))	parity\:\ln(\csc(x)-\cot(x))
derivative of 1/((2x^3+3x+1)^{3/4)}	derivative\:\frac{1}{(2x^{3}+3x+1)^{\frac{3}{4}}}
normal of y=e^{2x},\at x=ln(2)	normal\:y=e^{2x},\at\:x=\ln(2)
(\partial)/(\partial y)(ycos(xy)+e^x)	\frac{\partial\:}{\partial\:y}(y\cos(xy)+e^{x})
derivative of \sqrt[3]{3x^4+4x^3}	derivative\:\sqrt[3]{3x^{4}+4x^{3}}
integral of cos^2(t)-sin^2(t)	\int\:\cos^{2}(t)-\sin^{2}(t)dt
(\partial)/(\partial x)(sin(x^1y^3))	\frac{\partial\:}{\partial\:x}(\sin(x^{1}y^{3}))
expand (-2cos(2x)-sin(3x))^2	expand\:(-2\cos(2x)-\sin(3x))^{2}
limit as x approaches 1/2 of arcsin(x)	\lim\:_{x\to\:\frac{1}{2}}(\arcsin(x))

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