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Popular Calculus Problems

derivative of y=x(x^2+1)	derivative\:y=x(x^{2}+1)
f(y)=cos^2(y)	f(y)=\cos^{2}(y)
integral of sec^4(5x)tan^3(5x)	\int\:\sec^{4}(5x)\tan^{3}(5x)dx
f^'(x)= 1/(1+\frac{1){1+1/(1+x)}}	f^{\prime\:}(x)=\frac{1}{1+\frac{1}{1+\frac{1}{1+x}}}
derivative of (-3x+2^4(-2x+3)^3)	\frac{d}{dx}((-3x+2)^{4}(-2x+3)^{3})
derivative of f(x)=sqrt(x-5)	derivative\:f(x)=\sqrt{x-5}
y^{''}+2y^'+y=sin(x)+4cos(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\sin(x)+4\cos(2x)
(y+4)*(dy)/(dx)=2xy+4y	(y+4)\cdot\:\frac{dy}{dx}=2xy+4y
limit as x approaches pi of-csc(2x)	\lim\:_{x\to\:π}(-\csc(2x))
sum from n=0 to infinity of 2x^{2n}	\sum\:_{n=0}^{\infty\:}2x^{2n}
integral from 3 to infinity of e^{-x}	\int\:_{3}^{\infty\:}e^{-x}dx
integral from 0 to 0.9 of 1/(1-x)	\int\:_{0}^{0.9}\frac{1}{1-x}dx
(dy)/(dx)=2xe^{4y}	\frac{dy}{dx}=2xe^{4y}
derivative of ln(sqrt(x^2e^{x^{2+1)}})	\frac{d}{dx}(\ln(\sqrt{x^{2}e^{x^{2+1}}}))
integral of cot^5(x)csc^2(x)	\int\:\cot^{5}(x)\csc^{2}(x)dx
integral of 4cos(2θ)	\int\:4\cos(2θ)dθ
integral of r^2cos(θ)	\int\:r^{2}\cos(θ)dr
derivative of 4-2x^2	\frac{d}{dx}(4-2x^{2})
derivative of (x^3/(4-x^2))	\frac{d}{dx}(\frac{x^{3}}{4-x^{2}})
integral of 5sin(3x)sin(6x)	\int\:5\sin(3x)\sin(6x)dx
inverse oflaplace (15)/(3s+sqrt(3))	inverselaplace\:\frac{15}{3s+\sqrt{3}}
(dy)/(dt)+0.7ty=7t,y(0)=7	\frac{dy}{dt}+0.7ty=7t,y(0)=7
y^{''}+2y^'+2y=sin(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(2x)
integral of 8/(sqrt(4-x^2))	\int\:\frac{8}{\sqrt{4-x^{2}}}dx
integral of (x^2-1)/(x^3-3x+1)	\int\:\frac{x^{2}-1}{x^{3}-3x+1}dx
derivative of f(x)=e^{-0.5x}(4-x)-2	derivative\:f(x)=e^{-0.5x}(4-x)-2
sum from n=1 to infinity of 5/(4n^2-1)	\sum\:_{n=1}^{\infty\:}\frac{5}{4n^{2}-1}
integral from 1/5 to 7 of 8xln(5x)	\int\:_{\frac{1}{5}}^{7}8x\ln(5x)dx
y^'+2/x y=4x	y^{\prime\:}+\frac{2}{x}y=4x
derivative of ln(7x^2+5y^2)	\frac{d}{dx}(\ln(7x^{2}+5y^{2}))
derivative of 4t^{(-1)/8}+5ln(t)+ln(5)	derivative\:4t^{\frac{-1}{8}}+5\ln(t)+\ln(5)
tangent of f(x)=3x^2-4x+1	tangent\:f(x)=3x^{2}-4x+1
derivative of (9-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{9-\sec(x)}{\tan(x)})
integral of (x^3+5)	\int\:(x^{3}+5)dx
integral of e^{t/5}	\int\:e^{\frac{t}{5}}dt
limit as x approaches 2-of (x^2)/(x-2)	\lim\:_{x\to\:2-}(\frac{x^{2}}{x-2})
sum from n=1 to infinity of n^3(1+n^4)	\sum\:_{n=1}^{\infty\:}n^{3}(1+n^{4})
derivative of f(x)=x*e^{2x-4},x=2	derivative\:f(x)=x\cdot\:e^{2x-4},x=2
derivative of y= 4/(7x^2)	derivative\:y=\frac{4}{7x^{2}}
limit as x approaches 4 of sqrt(x^3+6x)	\lim\:_{x\to\:4}(\sqrt{x^{3}+6x})
limit as x approaches 2 of 3cos(x)	\lim\:_{x\to\:2}(3\cos(x))
d/(dt)(4t^2+2t+5)	\frac{d}{dt}(4t^{2}+2t+5)
derivative of e^{cos(x}+e^{sin(y)})	\frac{d}{dx}(e^{\cos(x)}+e^{\sin(y)})
derivative of log_{3}(5x-1)	\frac{d}{dx}(\log_{3}(5x-1))
derivative of 1/(2sqrt(r))+1/(9r^{8/9)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{9r^{\frac{8}{9}}}
integral of-9.8	\int\:-9.8dx
(\partial)/(\partial x)(11x^2y+8xy^3)	\frac{\partial\:}{\partial\:x}(11x^{2}y+8xy^{3})
derivative of 1/((4x^3))	\frac{d}{dx}(\frac{1}{(4x)^{3}})
integral from 1 to 2 of 1/(8-3x)	\int\:_{1}^{2}\frac{1}{8-3x}dx
integral of 8x^3+12x+2	\int\:8x^{3}+12x+2dx
(\partial)/(\partial x)(x^2y^2-3y)	\frac{\partial\:}{\partial\:x}(x^{2}y^{2}-3y)
area f(x)=4x+8,0,8	area\:f(x)=4x+8,0,8
sum from n=0 to infinity of (7n!)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{7n!}{2^{n}}
tangent of f(x)=1-x-x^2,\at x=0	tangent\:f(x)=1-x-x^{2},\at\:x=0
derivative of x(29-2x)(16-2x)	derivative\:x(29-2x)(16-2x)
integral of 9tan(x)sec(3)(x)	\int\:9\tan(x)\sec(3)(x)dx
f(x)=x^6e^x	f(x)=x^{6}e^{x}
derivative of sin(x)ln(8x)	derivative\:\sin(x)\ln(8x)
integral from-3 to 3 of (9-x^2)^2	\int\:_{-3}^{3}(9-x^{2})^{2}dx
integral of (1-x^2)/(x(x^2+1))	\int\:\frac{1-x^{2}}{x(x^{2}+1)}dx
integral of e^x+x^2	\int\:e^{x}+x^{2}dx
derivative of 3x^7	\frac{d}{dx}(3x^{7})
derivative of f(r)=sqrt(r)+\sqrt[7]{r}	derivative\:f(r)=\sqrt{r}+\sqrt[7]{r}
integral of (2xe^{-3x})	\int\:(2xe^{-3x})dx
y^'+2sin(2x)y=2sin(2x),y(pi/2)=3	y^{\prime\:}+2\sin(2x)y=2\sin(2x),y(\frac{π}{2})=3
limit as h approaches 0 of (-4)^2+2(-4)	\lim\:_{h\to\:0}((-4)^{2}+2(-4))
integral of (x^2)/(sqrt(21+4x-x^2))	\int\:\frac{x^{2}}{\sqrt{21+4x-x^{2}}}dx
inverse oflaplace ((s+9))/((s^2+6s+34))	inverselaplace\:\frac{(s+9)}{(s^{2}+6s+34)}
(dy)/(dx)-2/x y= 3/(x^2)y^4	\frac{dy}{dx}-\frac{2}{x}y=\frac{3}{x^{2}}y^{4}
integral from 1 to 2 of 13sqrt(4x^2-3)	\int\:_{1}^{2}13\sqrt{4x^{2}-3}dx
derivative of y=(4x-5)2	derivative\:y=(4x-5)2
integral of 7cot^4(5t)	\int\:7\cot^{4}(5t)dt
(\partial)/(\partial y)(y(-2x-y+1))	\frac{\partial\:}{\partial\:y}(y(-2x-y+1))
integral of x^2e^{-x}	\int\:x^{2}e^{-x}dx
integral of 24+cos(x)	\int\:24+\cos(x)dx
integral of x*e^{x/4}	\int\:x\cdot\:e^{\frac{x}{4}}dx
derivative of y=arctan(sqrt(7x^2-1))	derivative\:y=\arctan(\sqrt{7x^{2}-1})
integral of x(cos^2(x))	\int\:x(\cos^{2}(x))dx
(x^2+1)y^'+8x(y-1)=0,y(0)=3	(x^{2}+1)y^{\prime\:}+8x(y-1)=0,y(0)=3
(\partial)/(\partial x)(4x^2-4xy+xyz)	\frac{\partial\:}{\partial\:x}(4x^{2}-4xy+xyz)
integral of (t^2-1)(4+3t)	\int\:(t^{2}-1)(4+3t)dt
tangent of f(x)=x^4,\at x=1	tangent\:f(x)=x^{4},\at\:x=1
tangent of y= 6/(sqrt(x)),(25, 6/5)	tangent\:y=\frac{6}{\sqrt{x}},(25,\frac{6}{5})
limit as x approaches infinity of ((sqrt(2x^2+1)))/(3x-5)	\lim\:_{x\to\:\infty\:}(\frac{(\sqrt{2x^{2}+1})}{3x-5})
laplacetransform cos(t+pi/4)	laplacetransform\:\cos(t+\frac{π}{4})
x^2(dy)/(dx)-2xy=4y^4,y(1)= 1/3	x^{2}\frac{dy}{dx}-2xy=4y^{4},y(1)=\frac{1}{3}
xy^'+y^2+y=0	xy^{\prime\:}+y^{2}+y=0
derivative of f(x)=sin^2(x)+cos^2(x)	derivative\:f(x)=\sin^{2}(x)+\cos^{2}(x)
tangent of-4x^2-3x+2,\at x=-1	tangent\:-4x^{2}-3x+2,\at\:x=-1
integral of 22x	\int\:22xdx
(dy)/(dt)+0.4ty=5t,y(0)=6	\frac{dy}{dt}+0.4ty=5t,y(0)=6
integral of (-t)/((t+1)-sqrt(t+1))	\int\:\frac{-t}{(t+1)-\sqrt{t+1}}dt
integral of 36	\int\:36
derivative of 2sin^3(5x)	\frac{d}{dx}(2\sin^{3}(5x))
integral of 3x(ln(x^7))^2	\int\:3x(\ln(x^{7}))^{2}dx
derivative of arctan((3+x/(3-x)))	\frac{d}{dx}(\arctan(\frac{3+x}{3-x}))
derivative of x+{z}(x)	\frac{d}{dx}(x+{z}(x))
derivative of f(x)=-2sin(x)	derivative\:f(x)=-2\sin(x)
derivative of ln((cos(x)/(sin(x))))	\frac{d}{dx}(\ln(\frac{\cos(x)}{\sin(x)}))
integral of cos(ax+b)	\int\:\cos(ax+b)dx

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