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Popular Calculus Problems

integral of (2x^2+3x+6)/(x^3+4x)	\int\:\frac{2x^{2}+3x+6}{x^{3}+4x}dx
integral of ((x+1))/((x^2+1))	\int\:\frac{(x+1)}{(x^{2}+1)}dx
derivative of y=ln(sqrt(x+6))	derivative\:y=\ln(\sqrt{x+6})
integral of (sin(x))^4	\int\:(\sin(x))^{4}dx
derivative of \sqrt[5]{x}-5e^x	\frac{d}{dx}(\sqrt[5]{x}-5e^{x})
taylor x^{(1/3)},8	taylor\:x^{(\frac{1}{3})},8
integral of 2xsqrt(x^2+4)	\int\:2x\sqrt{x^{2}+4}dx
integral of 1/(sqrt(x^2+81))	\int\:\frac{1}{\sqrt{x^{2}+81}}dx
integral from 1 to x of sqrt(1+2t)	\int\:_{1}^{x}\sqrt{1+2t}dt
derivative of 4/3pix^3	\frac{d}{dx}(\frac{4}{3}\cdot\:π\cdot\:x^{3})
integral of x^35x	\int\:x^{3}5xdx
limit as x approaches 0 of (cos(6x))/1	\lim\:_{x\to\:0}(\frac{\cos(6x)}{1})
limit as x approaches 3 of (2x-6)/(x-3)	\lim\:_{x\to\:3}(\frac{2x-6}{x-3})
integral from 0 to pi of xsin(nx)	\int\:_{0}^{π}x\sin(nx)dx
y^'=sqrt(y),y(0)=0	y^{\prime\:}=\sqrt{y},y(0)=0
y^{''}-2y^'-3y=e^{-x}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=e^{-x}
derivative of sin^2(5x)	derivative\:\sin^{2}(5x)
dy+ydx=2xy^2e^xdx	dy+ydx=2xy^{2}e^{x}dx
derivative of 2^xx^2	\frac{d}{dx}(2^{x}x^{2})
integral of 1/(8-7x)	\int\:\frac{1}{8-7x}dx
integral of (x^2+2x)cos(x)	\int\:(x^{2}+2x)\cos(x)dx
derivative of sqrt((x^4))	\frac{d}{dx}(\sqrt{(x^{4})})
y^{''}+4y=5sin(2x)	y^{\prime\:\prime\:}+4y=5\sin(2x)
integral from 7 to infinity of xe^{-4x}	\int\:_{7}^{\infty\:}xe^{-4x}dx
derivative of 8e^x+4/(\sqrt[3]{x)}	derivative\:8e^{x}+\frac{4}{\sqrt[3]{x}}
(\partial)/(\partial x)(5(y-1)^3(x-4))	\frac{\partial\:}{\partial\:x}(5(y-1)^{3}(x-4))
limit as x approaches infinity+of 2/x-3	\lim\:_{x\to\:\infty\:+}(\frac{2}{x}-3)
(\partial)/(\partial x)(y-2x-2)	\frac{\partial\:}{\partial\:x}(y-2x-2)
integral of 2/(2t-1)	\int\:\frac{2}{2t-1}dt
integral of (2+ln(x))/x	\int\:\frac{2+\ln(x)}{x}dx
derivative of ln(1+2/x)	\frac{d}{dx}(\ln(1+\frac{2}{x}))
integral from-1 to 5 of (8y)/(y^2-4y-12)	\int\:_{-1}^{5}\frac{8y}{y^{2}-4y-12}dy
integral of 16csc(8x)sec(8x)	\int\:16\csc(8x)\sec(8x)dx
area x^2+2x+1,-1,7	area\:x^{2}+2x+1,-1,7
area y=8x,y=x^2-9	area\:y=8x,y=x^{2}-9
derivative of (400/(1+39e^{-0.16x)})	\frac{d}{dx}(\frac{400}{1+39e^{-0.16x}})
integral of (3+t+t^2)/(sqrt(t))	\int\:\frac{3+t+t^{2}}{\sqrt{t}}dt
integral from 5 to 9 of (x-4)/(x^2)	\int\:_{5}^{9}\frac{x-4}{x^{2}}dx
derivative of 7sqrt(x)+5	\frac{d}{dx}(7\sqrt{x}+5)
integral from 0 to 1 of (5t^4)/(1+t^5)	\int\:_{0}^{1}\frac{5t^{4}}{1+t^{5}}dt
integral of 1/(y(y+2))	\int\:\frac{1}{y(y+2)}dy
derivative of-2sin(x)	derivative\:-2\sin(x)
integral of 1/(x^2sqrt(1+x^2))	\int\:\frac{1}{x^{2}\sqrt{1+x^{2}}}dx
integral of (8x)/(2x^2+1)	\int\:\frac{8x}{2x^{2}+1}dx
derivative of y=(x+1)^3	derivative\:y=(x+1)^{3}
integral of x/(sqrt(x^2-2))	\int\:\frac{x}{\sqrt{x^{2}-2}}dx
integral of 1/(16+25x^2)	\int\:\frac{1}{16+25x^{2}}dx
integral of (x+1)/(sqrt(x))	\int\:\frac{x+1}{\sqrt{x}}dx
integral of 1/(x*sqrt(x^2+1))	\int\:\frac{1}{x\cdot\:\sqrt{x^{2}+1}}dx
integral from 1 to 5 of (x+1)sqrt(2x-1)	\int\:_{1}^{5}(x+1)\sqrt{2x-1}dx
integral of 4/(2x+3)	\int\:\frac{4}{2x+3}dx
derivative of (t-sqrt(t))/(t^{1/3)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{3}}}
(\partial)/(\partial y)(4y^3)	\frac{\partial\:}{\partial\:y}(4y^{3})
integral of xarcsin(2)x^2	\int\:x\arcsin(2)x^{2}dx
(dy)/(dx)=y^{2/3}	\frac{dy}{dx}=y^{\frac{2}{3}}
integral from 0 to 1 of (69)/(x^5)	\int\:_{0}^{1}\frac{69}{x^{5}}dx
derivative of 5tsin(pit)	derivative\:5t\sin(πt)
area y=e^{2x},y=e^{3x},x=1	area\:y=e^{2x},y=e^{3x},x=1
limit as x approaches-6 of sqrt(-5x-6)	\lim\:_{x\to\:-6}(\sqrt{-5x-6})
tangent of f(x)=(2x)/(x^2-7),\at x=3	tangent\:f(x)=\frac{2x}{x^{2}-7},\at\:x=3
integral of (sin(3x))/(3cos(3x))	\int\:\frac{\sin(3x)}{3\cos(3x)}dx
integral of x^2e^{15x}	\int\:x^{2}e^{15x}dx
integral of (1+3t)t^2	\int\:(1+3t)t^{2}dt
limit as x approaches infinity of xe^{-x}	\lim\:_{x\to\:\infty\:}(xe^{-x})
derivative of tan(0)	\frac{d}{dx}(\tan(0))
(\partial)/(\partial x)(y^3)	\frac{\partial\:}{\partial\:x}(y^{3})
simplify in(sin(x))	simplify\:in(\sin(x))
derivative of 1/(csc^2(x))	\frac{d}{dx}(\frac{1}{\csc^{2}(x)})
integral of 1/(2x^2+8x+25)	\int\:\frac{1}{2x^{2}+8x+25}dx
(dy}{dx}=-\frac{5x)/y	\frac{dy}{dx}=-\frac{5x}{y}
derivative of e^{tan(2x+1})	\frac{d}{dx}(e^{\tan(2x+1)})
limit as x approaches 5-of \|x-5\|	\lim\:_{x\to\:5-}(\left\|x-5\right\|)
integral of-cos(x)+sin(x)+2	\int\:-\cos(x)+\sin(x)+2dx
derivative of sqrt(-5x+5)	\frac{d}{dx}(\sqrt{-5x+5})
limit as x approaches 9+of ln(x-9)	\lim\:_{x\to\:9+}(\ln(x-9))
(\partial)/(\partial x)((x^2-1)/(x+1))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-1}{x+1})
y^{''}+2y^'+y=(-18.5e^{-t})/(t^2+1)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\frac{-18.5e^{-t}}{t^{2}+1}
integral of cos(3x)sin(3x)	\int\:\cos(3x)\sin(3x)dx
(\partial)/(\partial x)(7+ln(xy-9))	\frac{\partial\:}{\partial\:x}(7+\ln(xy-9))
derivative of e^{ax^9}	\frac{d}{dx}(e^{ax^{9}})
d/(dy)(e^xcos(y))	\frac{d}{dy}(e^{x}\cos(y))
(\partial)/(\partial x)((26)/((2+x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{26}{(2+x^{2}+y^{2})})
integral of e^x*7x	\int\:e^{x}\cdot\:7xdx
(u^2+u)dx+u^2(xdu+udx)=0	(u^{2}+u)dx+u^{2}(xdu+udx)=0
limit as x approaches 4 of e^x+4x	\lim\:_{x\to\:4}(e^{x}+4x)
integral of 3sqrt(2x)	\int\:3\sqrt{2x}dx
(\partial)/(\partial x)(7xsin(5x^2y))	\frac{\partial\:}{\partial\:x}(7x\sin(5x^{2}y))
integral of sqrt(x)sqrt(x\sqrt{x)+1}	\int\:\sqrt{x}\sqrt{x\sqrt{x}+1}dx
y^{''}+4y^'+3y=15te^{3t}	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=15te^{3t}
area x^2=4y,3x-4y+4=0	area\:x^{2}=4y,3x-4y+4=0
y^'+y=e^{-t}sin(t),y(0)=1	y^{\prime\:}+y=e^{-t}\sin(t),y(0)=1
y^'=sqrt(y)(1-sqrt(y))	y^{\prime\:}=\sqrt{y}(1-\sqrt{y})
limit as x approaches-4 of 8x^2+1	\lim\:_{x\to\:-4}(8x^{2}+1)
taylor-2sin(4x)	taylor\:-2\sin(4x)
derivative of y=ln(x^8)	derivative\:y=\ln(x^{8})
integral of-csc^2((8x)/5)	\int\:-\csc^{2}(\frac{8x}{5})dx
(dy)/(dx)=x^5(y-3),y(0)=5	\frac{dy}{dx}=x^{5}(y-3),y(0)=5
integral of (x+1)(x+2)^6	\int\:(x+1)(x+2)^{6}dx
integral of 5x^4-4x^5	\int\:5x^{4}-4x^{5}dx
derivative of 35+35sin((-2pit-pi)/2)	derivative\:35+35\sin(\frac{-2πt-π}{2})

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