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Popular Calculus Problems

integral of 1/(sqrt(x^2+6x+25))	\int\:\frac{1}{\sqrt{x^{2}+6x+25}}dx
maclaurin 1/(x+1)	maclaurin\:\frac{1}{x+1}
integral of (\sqrt[3]{x^2}+1)	\int\:(\sqrt[3]{x^{2}}+1)dx
integral of sin^2((pix)/L)	\int\:\sin^{2}(\frac{πx}{L})dx
t^2y^{''}-3ty^'+4y=0	t^{2}y^{\prime\:\prime\:}-3ty^{\prime\:}+4y=0
(\partial)/(\partial y)((x+y)^5+(x-y)^5)	\frac{\partial\:}{\partial\:y}((x+y)^{5}+(x-y)^{5})
tangent of f(x)=x^2+5,(-5,30)	tangent\:f(x)=x^{2}+5,(-5,30)
xy^{''}-2y^'+4=0	xy^{\prime\:\prime\:}-2y^{\prime\:}+4=0
slope of (-3.7)(-4.12)	slope\:(-3.7)(-4.12)
tangent of f(x)=x^3(3-x)^4,\at x=2	tangent\:f(x)=x^{3}(3-x)^{4},\at\:x=2
limit as x approaches 100 of 20+0.188x	\lim\:_{x\to\:100}(20+0.188x)
integral of ysqrt(6+12y-36y^2)	\int\:y\sqrt{6+12y-36y^{2}}dy
derivative of (-1+x^2^{-1})	\frac{d}{dx}((-1+x^{2})^{-1})
integral from 1 to 5 of 6xln(x)	\int\:_{1}^{5}6x\ln(x)dx
integral of cos(x+nx)	\int\:\cos(x+nx)dx
(dy)/(dt)=ysin(t)	\frac{dy}{dt}=y\sin(t)
integral of (5+u)/u	\int\:\frac{5+u}{u}du
derivative of \sqrt[3]{1+\sqrt[3]{1+\sqrt[3]{x}}}	\frac{d}{dx}(\sqrt[3]{1+\sqrt[3]{1+\sqrt[3]{x}}})
integral from-2 to 2 of 1/(x^2-1)	\int\:_{-2}^{2}\frac{1}{x^{2}-1}dx
integral of (18)/x	\int\:\frac{18}{x}dx
tangent of f(x)=x^2-2x,\at x=3	tangent\:f(x)=x^{2}-2x,\at\:x=3
(\partial)/(\partial y)(e^x+ye^{xy})	\frac{\partial\:}{\partial\:y}(e^{x}+ye^{xy})
(\partial)/(\partial x)(e^y+x+x^2+2)	\frac{\partial\:}{\partial\:x}(e^{y}+x+x^{2}+2)
(dy)/(-yln(y/k))=cdx	\frac{dy}{-y\ln(\frac{y}{k})}=cdx
(dy)/(dx)+3y=30	\frac{dy}{dx}+3y=30
y^{''}+9y=-6tan(3x)	y^{\prime\:\prime\:}+9y=-6\tan(3x)
derivative of (2(e^{3sqrt(x)}))	\frac{d}{dx}((2)(e^{3\sqrt{x}}))
integral from 0 to 1 of t^2cos(npit)	\int\:_{0}^{1}t^{2}\cos(nπt)dt
(dy)/(dx)=sin^2(x)	\frac{dy}{dx}=\sin^{2}(x)
integral from 1 to 2 of x/((x+1)^2)	\int\:_{1}^{2}\frac{x}{(x+1)^{2}}dx
derivative of 3/((x+2^2))	\frac{d}{dx}(\frac{3}{(x+2)^{2}})
y^'=e^{4x}-3x	y^{\prime\:}=e^{4x}-3x
derivative of 2cot(x/2)	\frac{d}{dx}(2\cot(\frac{x}{2}))
y^'=x^2-y	y^{\prime\:}=x^{2}-y
36y^{''}-y=xe^{x/6},y(0)=1,y^'(0)=0	36y^{\prime\:\prime\:}-y=xe^{\frac{x}{6}},y(0)=1,y^{\prime\:}(0)=0
f^'(x)=1	f^{\prime\:}(x)=1
integral of 64x	\int\:64xdx
tangent of 2x^3+8x^2-5x+9	tangent\:2x^{3}+8x^{2}-5x+9
area 8-2x,x^3-7x^2+12x,[1,4]	area\:8-2x,x^{3}-7x^{2}+12x,[1,4]
limit as h approaches 0 of sqrt(h)	\lim\:_{h\to\:0}(\sqrt{h})
integral from 1 to 3 of 9r^3ln(r)	\int\:_{1}^{3}9r^{3}\ln(r)dr
(sec^3(x))^'	(\sec^{3}(x))^{\prime\:}
integral of sin(-7x)	\int\:\sin(-7x)dx
integral from 0 to 2 of (x^3)/2	\int\:_{0}^{2}\frac{x^{3}}{2}dx
(\partial)/(\partial x)(sqrt(x)e^{xy})	\frac{\partial\:}{\partial\:x}(\sqrt{x}e^{xy})
y^'=(xy(4-y))/(1+x)	y^{\prime\:}=\frac{xy(4-y)}{1+x}
derivative of x^4-25x^2+144	\frac{d}{dx}(x^{4}-25x^{2}+144)
(\partial)/(\partial x)(x(x^2+y^2)^{1/2})	\frac{\partial\:}{\partial\:x}(x(x^{2}+y^{2})^{\frac{1}{2}})
derivative of y=9e^{9e^x+x}	derivative\:y=9e^{9e^{x}+x}
derivative of 1+e^x	derivative\:1+e^{x}
y^{''}+2y^'+y=8e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=8e^{-t}
(dy)/(dx)=-(2xy+y^2+1)/(x^2+2xy)	\frac{dy}{dx}=-\frac{2xy+y^{2}+1}{x^{2}+2xy}
sum from k=1 to infinity of (2^k)/(k!)	\sum\:_{k=1}^{\infty\:}\frac{2^{k}}{k!}
derivative of x^2e^y	\frac{d}{dx}(x^{2}e^{y})
derivative of sqrt(x)-4\sqrt[3]{x}	derivative\:\sqrt{x}-4\sqrt[3]{x}
integral of s4^s	\int\:s4^{s}ds
integral from 0 to pi/2 of (cos(x))^2	\int\:_{0}^{\frac{π}{2}}(\cos(x))^{2}dx
sum from n=1 to infinity of 4^{1/(2^n)}	\sum\:_{n=1}^{\infty\:}4^{\frac{1}{2^{n}}}
derivative of y=(2^x)^8	derivative\:y=(2^{x})^{8}
integral of (x^2+2)^42x	\int\:(x^{2}+2)^{4}2xdx
4y^{''}+4y^'+8y=0	4y^{\prime\:\prime\:}+4y^{\prime\:}+8y=0
limit as x approaches 0 of cos(9x)	\lim\:_{x\to\:0}(\cos(9x))
sum from n=1 to infinity of n2^{-n}	\sum\:_{n=1}^{\infty\:}n2^{-n}
integral of xye^{y^2x}	\int\:xye^{y^{2}x}dy
derivative of 3/(e^x+e^{-x)}	derivative\:\frac{3}{e^{x}+e^{-x}}
derivative of ke^x	\frac{d}{dx}(ke^{x})
xsin(y/x)(dy)/(dx)=ysin(y/x)+x	x\sin(\frac{y}{x})\frac{dy}{dx}=y\sin(\frac{y}{x})+x
integral of 1/(a^2+v^2)	\int\:\frac{1}{a^{2}+v^{2}}dv
limit as x approaches 4+of 2/(x-4)	\lim\:_{x\to\:4+}(\frac{2}{x-4})
integral from 1 to e^5 of x^2ln(x)	\int\:_{1}^{e^{5}}x^{2}\ln(x)dx
integral of 1/((2x)^3)	\int\:\frac{1}{(2x)^{3}}dx
-10x^2y+(dy)/(dx)=9x^2	-10x^{2}y+\frac{dy}{dx}=9x^{2}
integral of 3θcos(θ)	\int\:3θ\cos(θ)dθ
derivative of (x^2-8/(x-3))	\frac{d}{dx}(\frac{x^{2}-8}{x-3})
2y^{''}-4y^'+4y=e^xsec(x)	2y^{\prime\:\prime\:}-4y^{\prime\:}+4y=e^{x}\sec(x)
integral of csc^2(x	\int\:\csc^{2}(d)xdx
integral of (2y-1)/(x^2+1)	\int\:\frac{2y-1}{x^{2}+1}dy
integral of In\sqrt[3]{x}	\int\:In\sqrt[3]{x}dx
integral of 1/(sqrt(3x))	\int\:\frac{1}{\sqrt{3x}}dx
derivative of cos(x^{sin(x}))	\frac{d}{dx}(\cos(x^{\sin(x)}))
derivative of x^4-50x^2	\frac{d}{dx}(x^{4}-50x^{2})
(\partial)/(\partial x)(2x^2+2y-8)	\frac{\partial\:}{\partial\:x}(2x^{2}+2y-8)
tangent of f(x)=sqrt(5x+6),(2,4)	tangent\:f(x)=\sqrt{5x+6},(2,4)
laplacetransform t*sin(t)	laplacetransform\:t\cdot\:\sin(t)
derivative of sin(2x+3ln(e)+4sqrt(x))	\frac{d}{dx}(\sin(2x)+3\ln(e)+4\sqrt{x})
slope of (4,2),(3,-1)	slope\:(4,2),(3,-1)
(\partial)/(\partial θ)(cos^2(θ))	\frac{\partial\:}{\partial\:θ}(\cos^{2}(θ))
integral of (cos(θ))^3	\int\:(\cos(θ))^{3}dθ
integral from 0 to pi/3 of xsin(x+y)	\int\:_{0}^{\frac{π}{3}}x\sin(x+y)dy
integral of sin(x)+3cos(x)	\int\:\sin(x)+3\cos(x)dx
derivative of sqrt((1+2x))	\frac{d}{dx}(\sqrt{(1+2x)})
limit as x approaches 4-of 3/(x^2-16)	\lim\:_{x\to\:4-}(\frac{3}{x^{2}-16})
derivative of y=tan(2)(x)	derivative\:y=\tan(2)(x)
derivative of 3arcsin(x^4)	derivative\:3\arcsin(x^{4})
derivative of-131072sin(2x)	\frac{d}{dx}(-131072\sin(2x))
limit as x approaches (-1^+) of 4x^3-2m	\lim\:_{x\to\:(-1^{+})}(4x^{3}-2m)
derivative of ln(3x^3+2)	derivative\:\ln(3x^{3}+2)
(\partial)/(\partial r)(2t+r^2cos(t))	\frac{\partial\:}{\partial\:r}(2t+r^{2}\cos(t))
integral of (e^{4x})/(1+e^{2x)}	\int\:\frac{e^{4x}}{1+e^{2x}}dx
integral from 0 to infinity of x/(e^x)	\int\:_{0}^{\infty\:}\frac{x}{e^{x}}dx

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