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Popular Calculus Problems

integral of 1/(x^2+6x+16)	\int\:\frac{1}{x^{2}+6x+16}dx
limit as x approaches 0 of (sin(x))/(9x)	\lim\:_{x\to\:0}(\frac{\sin(x)}{9x})
6x^2y^{''}+13xy^'+y=70x+2	6x^{2}y^{\prime\:\prime\:}+13xy^{\prime\:}+y=70x+2
integral from-2 to 1 of 2x+4	\int\:_{-2}^{1}2x+4dx
derivative of 2x(1-x^2^{1/2})	\frac{d}{dx}(2x(1-x^{2})^{\frac{1}{2}})
x(dy)/(dx)+2y=4e^x	x\frac{dy}{dx}+2y=4e^{x}
integral of 3xy^2sec^2(2xy)	\int\:3xy^{2}\sec^{2}(2xy)dx
integral of 5x^{4/3}+2x^{5/4}	\int\:5x^{\frac{4}{3}}+2x^{\frac{5}{4}}dx
derivative of 4+3x-2x^3	\frac{d}{dx}(4+3x-2x^{3})
derivative of (12x/((x^2+2)^2))	\frac{d}{dx}(\frac{12x}{(x^{2}+2)^{2}})
derivative of f(x)=ln(x^2+4)	derivative\:f(x)=\ln(x^{2}+4)
y^'-2y=0	y^{\prime\:}-2y=0
derivative of ln(arctan(2x))	\frac{d}{dx}(\ln(\arctan(2x)))
limit as x approaches 0+of x^{8sin(x)}	\lim\:_{x\to\:0+}(x^{8\sin(x)})
derivative of 1/(sqrt(2))	\frac{d}{dx}(\frac{1}{\sqrt{2}})
deg2rad (x'-4x)^'	deg2rad\:(x\prime\:-4x)^{\prime\:}
integral of 1/(25e^{-8x)+e^{8x}}	\int\:\frac{1}{25e^{-8x}+e^{8x}}dx
derivative of f(x)=-4x^2+7x-5	derivative\:f(x)=-4x^{2}+7x-5
integral of (3-1/(x^4)+1/(x^2))	\int\:(3-\frac{1}{x^{4}}+\frac{1}{x^{2}})dx
derivative of sqrt(2)u+sqrt(3u)	derivative\:\sqrt{2}u+\sqrt{3u}
integral of x^2*log_{3}(x)	\int\:x^{2}\cdot\:\log_{3}(x)dx
y^{''}-y^'-6y=0	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0
integral of 9sin^4(x)	\int\:9\sin^{4}(x)dx
integral of sin^{12}(x)cos(x)	\int\:\sin^{12}(x)\cos(x)dx
limit as x approaches 0 of (1+5x)^{2/x}	\lim\:_{x\to\:0}((1+5x)^{\frac{2}{x}})
(dy)/(dx)=k_{1}(y-c_{1})	\frac{dy}{dx}=k_{1}(y-c_{1})
derivative of cos(X)	derivative\:\cos(X)
x^3y^{'''}+6x^2y^{''}+7xy^'+y=0	x^{3}y^{\prime\:\prime\:\prime\:}+6x^{2}y^{\prime\:\prime\:}+7xy^{\prime\:}+y=0
derivative of (cos(x))/(1-sin(x))	derivative\:\frac{\cos(x)}{1-\sin(x)}
x^2((dy)/(dx))+x(x+2)y=e^x	x^{2}(\frac{dy}{dx})+x(x+2)y=e^{x}
f(x)=sec(4x)	f(x)=\sec(4x)
integral of x*ln(x^6)	\int\:x\cdot\:\ln(x^{6})dx
limit as x approaches infinity of 9+8/x	\lim\:_{x\to\:\infty\:}(9+\frac{8}{x})
integral of 2te^{-2t}	\int\:2te^{-2t}dt
integral of (e^{2x^2})	\int\:(e^{2x^{2}})dx
integral of (sin(ln(x^3)))/x	\int\:\frac{\sin(\ln(x^{3}))}{x}dx
roots ae^{3x}	roots\:ae^{3x}
derivative of g(x)=(x+2sqrt(x))e^x	derivative\:g(x)=(x+2\sqrt{x})e^{x}
(d^3)/(dx^3)(1/(x^2+1))	\frac{d^{3}}{dx^{3}}(\frac{1}{x^{2}+1})
tangent of 8x^2+3x-7	tangent\:8x^{2}+3x-7
integral from-1 to 1 of (x+1)(x+2)(x+3)	\int\:_{-1}^{1}(x+1)(x+2)(x+3)dx
derivative of 8(e^0cos(0)-e^0sin(0))	derivative\:8(e^{0}\cos(0)-e^{0}\sin(0))
tangent of (x^2)/(x+9)	tangent\:\frac{x^{2}}{x+9}
integral of (3-2x)/(5x^2+7)	\int\:\frac{3-2x}{5x^{2}+7}dx
integral from-1 to 3 of (x^3-2)	\int\:_{-1}^{3}(x^{3}-2)dx
integral of-2y^2	\int\:-2y^{2}dy
limit as x approaches 0 of x/3	\lim\:_{x\to\:0}(\frac{x}{3})
integral of ((x^2+1)^2)/(sqrt(x))	\int\:\frac{(x^{2}+1)^{2}}{\sqrt{x}}dx
tangent of 4sin(x)	tangent\:4\sin(x)
derivative of 5x^{2/3}	\frac{d}{dx}(5x^{\frac{2}{3}})
3yy^'+2x=0	3yy^{\prime\:}+2x=0
derivative of 5/(sqrt((7-x^2^5)))	\frac{d}{dx}(\frac{5}{\sqrt{(7-x^{2})^{5}}})
derivative of 12x^5-8x^4+20x^3	derivative\:12x^{5}-8x^{4}+20x^{3}
derivative of (sin(2x+1)/(cos(-1-2x)))	\frac{d}{dx}(\frac{\sin(2x+1)}{\cos(-1-2x)})
(d^2)/(dx^2)(cos(6x))	\frac{d^{2}}{dx^{2}}(\cos(6x))
limit as x approaches-1 of x(0)	\lim\:_{x\to\:-1}(x(0))
limit as x approaches 0 of 3f(x)(x^2)	\lim\:_{x\to\:0}(3f(x)(x^{2}))
integral of cos(sqrt(3x))	\int\:\cos(\sqrt{3x})dx
limit as x approaches 0+of xln(2x)	\lim\:_{x\to\:0+}(x\ln(2x))
integral of v^{1/2}	\int\:v^{\frac{1}{2}}dv
integral of (x+2)(x-1)	\int\:(x+2)(x-1)dx
limit as x approaches 0-of x^9-1/x	\lim\:_{x\to\:0-}(x^{9}-\frac{1}{x})
integral of (9x+11)e^x	\int\:(9x+11)e^{x}dx
integral of 1/(xsqrt(1+3x))	\int\:\frac{1}{x\sqrt{1+3x}}dx
integral of x/(x^2-1)	\int\:\frac{x}{x^{2}-1}dx
limit as x approaches 3 of sqrt(x+1)-2	\lim\:_{x\to\:3}(\sqrt{x+1}-2)
integral of csc(u)	\int\:\csc(u)du
derivative of (-y/(x^2+y^2))	\frac{d}{dx}(\frac{-y}{x^{2}+y^{2}})
integral of 5\sqrt[4]{e^x}	\int\:5\sqrt[4]{e^{x}}dx
taylor 2^x	taylor\:2^{x}
integral of (x^2+48x-16)/(x^3-16x)	\int\:\frac{x^{2}+48x-16}{x^{3}-16x}dx
derivative of 2^x+1	\frac{d}{dx}(2^{x}+1)
(dy)/(dt)=-y/(t^2)	\frac{dy}{dt}=-\frac{y}{t^{2}}
tangent of f(x)=6x-x^2,\at x=4	tangent\:f(x)=6x-x^{2},\at\:x=4
derivative of (x-5sin(x))	\frac{d}{dx}((x-5)\sin(x))
sum from n=0 to infinity of 1/(1.5^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{1.5^{n}}
integral of-x^2-2x	\int\:-x^{2}-2xdx
integral of 1/(e^{6x)}	\int\:\frac{1}{e^{6x}}dx
(dP)/(dt)=50P-1/10 P	\frac{dP}{dt}=50P-\frac{1}{10}P
integral of (cos(2t))/2	\int\:\frac{\cos(2t)}{2}dt
derivative of (e^x/(e^x-1))	\frac{d}{dx}(\frac{e^{x}}{e^{x}-1})
integral of ln(x^2+x)	\int\:\ln(x^{2}+x)dx
(\partial)/(\partial x)(zarctan(yx))	\frac{\partial\:}{\partial\:x}(z\arctan(yx))
integral of 1/(4e^{-3x)+e^{3x}}	\int\:\frac{1}{4e^{-3x}+e^{3x}}dx
integral from-2 to 1 of (x-6\|x\|)	\int\:_{-2}^{1}(x-6\left\|x\right\|)dx
limit as x approaches 0 of-x^4	\lim\:_{x\to\:0}(-x^{4})
y^{''}+4y=x-(x^2)/(20)	y^{\prime\:\prime\:}+4y=x-\frac{x^{2}}{20}
derivative of ln((x^4/((3x-4)^2)))	\frac{d}{dx}(\ln(\frac{x^{4}}{(3x-4)^{2}}))
derivative of 2pix^2	derivative\:2πx^{2}
y^'+1/(200+t)y=0	y^{\prime\:}+\frac{1}{200+t}y=0
limit as x approaches 1+of x^2-1	\lim\:_{x\to\:1+}(x^{2}-1)
derivative of f(x)=ln(ln(4x))	derivative\:f(x)=\ln(\ln(4x))
(dx)/(dy)=(y-x)/(y+x)	\frac{dx}{dy}=\frac{y-x}{y+x}
(1+x^2)y^{''}=-2xy^'	(1+x^{2})y^{\prime\:\prime\:}=-2xy^{\prime\:}
(\partial)/(\partial θ)(e^rcos(θ))	\frac{\partial\:}{\partial\:θ}(e^{r}\cos(θ))
integral from 2 to 4 of 2/x-1/8 x	\int\:_{2}^{4}\frac{2}{x}-\frac{1}{8}xdx
derivative of y=-8x^3+9x^2+6x-5	derivative\:y=-8x^{3}+9x^{2}+6x-5
sum from n=0 to infinity of (3^n)/(n^3)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{n^{3}}
6y^'=y^2	6y^{\prime\:}=y^{2}
sum from n=2 to infinity of 2/(n^3-n)	\sum\:_{n=2}^{\infty\:}\frac{2}{n^{3}-n}

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