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Popular Calculus Problems

sum from n=2 to infinity of n/((n-1)!)	\sum\:_{n=2}^{\infty\:}\frac{n}{(n-1)!}
integral from 0 to 1 of cos(x^3)	\int\:_{0}^{1}\cos(x^{3})dx
integral of-5sin(5x)	\int\:-5\sin(5x)dx
f(y)=4y^2	f(y)=4y^{2}
derivative of xlog_{2}(x-3)	\frac{d}{dx}(x\log_{2}(x-3))
(ln(t))^'	(\ln(t))^{\prime\:}
derivative of (3x-5)/(x^2-1)	derivative\:\frac{3x-5}{x^{2}-1}
limit as x approaches-2 of (x^3)(5-3x^2)	\lim\:_{x\to\:-2}((x^{3})(5-3x^{2}))
derivative of sin(3x+cos(6x))	\frac{d}{dx}(\sin(3x)+\cos(6x))
integral of e^{iwt}	\int\:e^{iwt}dt
derivative of 1-((x+b+c/((3a))))	\frac{d}{dx}(1-(\frac{x+b+c}{(3a)}))
integral from 3 to 5 of 1/(x+1)	\int\:_{3}^{5}\frac{1}{x+1}dx
derivative of 1/2 e^{-x/2}	\frac{d}{dx}(\frac{1}{2}e^{-\frac{x}{2}})
y^'=(cos(14x))/(e^{14y)}	y^{\prime\:}=\frac{\cos(14x)}{e^{14y}}
derivative of ((x)/(sqrt(x^2+1)))	\frac{d}{dx}(\frac{(x)}{\sqrt{x^{2}+1}})
limit as x approaches x of x	\lim\:_{x\to\:x}(x)
tangent of y=(5x-1)(4+3x)x,\at x=0	tangent\:y=(5x-1)(4+3x)x,\at\:x=0
sum from n=1 to infinity of 7/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{7}{3^{n}}
derivative of x^2+(16/x)	\frac{d}{dx}(x^{2}+\frac{16}{x})
y^{''}+2y^'+5y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=0,y(0)=1,y^{\prime\:}(0)=1
derivative of (x+1^{sin(x)})	\frac{d}{dx}((x+1)^{\sin(x)})
2(dy)/(dx)=y-e^{4x}	2\frac{dy}{dx}=y-e^{4x}
slope of f(x)=sqrt(6x)(6.6)	slope\:f(x)=\sqrt{6x}(6.6)
(\partial)/(\partial y)(xsin(x+2y))	\frac{\partial\:}{\partial\:y}(x\sin(x+2y))
y^{''}-2y^'-8y=7-e^{4x}	y^{\prime\:\prime\:}-2y^{\prime\:}-8y=7-e^{4x}
tangent of f(x)=x^3+9x^2+34x+15,\at x=7	tangent\:f(x)=x^{3}+9x^{2}+34x+15,\at\:x=7
maclaurin cos(x^2)	maclaurin\:\cos(x^{2})
derivative of e^{-x^2}+x	\frac{d}{dx}(e^{-x^{2}}+x)
tangent of g(x)=3sqrt(x),\at x=4	tangent\:g(x)=3\sqrt{x},\at\:x=4
derivative of sqrt(y)	derivative\:\sqrt{y}
derivative of ((-3x^2)/(((x^2-2x+1))))	\frac{d}{dx}(\frac{(-3x^{2})}{((x^{2}-2x+1))})
integral from 1 to infinity of x/(9+x^2)	\int\:_{1}^{\infty\:}\frac{x}{9+x^{2}}dx
limit as x approaches 2 of (g(x))/(h(x))	\lim\:_{x\to\:2}(\frac{g(x)}{h(x)})
integral of sin^6(θ)	\int\:\sin^{6}(θ)dθ
limit as x approaches infinity of x^2-3x	\lim\:_{x\to\:\infty\:}(x^{2}-3x)
derivative of 50sin(2000x)	\frac{d}{dx}(50\sin(2000x))
area x=y^2-2,x=-y^2+2	area\:x=y^{2}-2,x=-y^{2}+2
integral of (8x)/(sqrt(x-1))	\int\:\frac{8x}{\sqrt{x-1}}dx
y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-25/3	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=-\frac{25}{3}
integral of ((x+2))/x	\int\:\frac{(x+2)}{x}dx
derivative of a^xln(x)	\frac{d}{dx}(a^{x}\ln(x))
11x-4ysqrt(x^2+1)(dy)/(dx)=0	11x-4y\sqrt{x^{2}+1}\frac{dy}{dx}=0
derivative of f(t)=sqrt(4t^2-t)	derivative\:f(t)=\sqrt{4t^{2}-t}
limit as x approaches 1 of x^2-x	\lim\:_{x\to\:1}(x^{2}-x)
tangent of 9x^2-x^3	tangent\:9x^{2}-x^{3}
derivative of 2(pi-e^4)	\frac{d}{dx}(2(π-e)^{4})
tangent of y=e^{-9t}	tangent\:y=e^{-9t}
sum from n=3 to infinity of 2^{-n+2}	\sum\:_{n=3}^{\infty\:}2^{-n+2}
integral of (cot^2(11x))/(sec(11x))	\int\:\frac{\cot^{2}(11x)}{\sec(11x)}dx
2y'-y^2+4=0	2y\prime\:-y^{2}+4=0
integral of t/(t^4+25)	\int\:\frac{t}{t^{4}+25}dt
integral of (2x+1)/(x^2+x-3)	\int\:\frac{2x+1}{x^{2}+x-3}dx
integral of (ln(x^5))/x	\int\:\frac{\ln(x^{5})}{x}dx
laplacetransform 2/3 t^2+5e^{-4t}	laplacetransform\:\frac{2}{3}t^{2}+5e^{-4t}
limit as x approaches infinity of ln(3x)	\lim\:_{x\to\:\infty\:}(\ln(3x))
tangent of f(x)=(16x)/(x^2+16),\at x=-2	tangent\:f(x)=\frac{16x}{x^{2}+16},\at\:x=-2
maclaurin sin(x^2)	maclaurin\:\sin(x^{2})
integral of ((x^3))/(sqrt(x^2+4))	\int\:\frac{(x^{3})}{\sqrt{x^{2}+4}}dx
(dy)/(dx)=e^{3x}	\frac{dy}{dx}=e^{3x}
laplacetransform 4(t-2)	laplacetransform\:4(t-2)
integral of-2y^3	\int\:-2y^{3}dy
derivative of (1-6ln(x)/(x^7))	\frac{d}{dx}(\frac{1-6\ln(x)}{x^{7}})
derivative of (sin(x)^{1/x})	\frac{d}{dx}((\sin(x))^{\frac{1}{x}})
derivative of x^{-6}	derivative\:x^{-6}
sum from n=1 to infinity}(-1)^{n+1 of (1/n+1/(3^n))	\sum\:_{n=1}^{\infty\:}(-1)^{n+1}(\frac{1}{n}+\frac{1}{3^{n}})
(\partial)/(\partial x)(1/(1-x))	\frac{\partial\:}{\partial\:x}(\frac{1}{1-x})
y^{''}+(-2a)y^'+(a^2)y=0	y^{\prime\:\prime\:}+(-2a)y^{\prime\:}+(a^{2})y=0
limit as x approaches 5-of 3/(5-x)	\lim\:_{x\to\:5-}(\frac{3}{5-x})
(\partial)/(\partial y)(y+yln(xy))	\frac{\partial\:}{\partial\:y}(y+y\ln(xy))
integral from 0 to 2 of t^3(1+t^4)^3	\int\:_{0}^{2}t^{3}(1+t^{4})^{3}dt
tangent of f(x)=sqrt(x),(-1,1)	tangent\:f(x)=\sqrt{x},(-1,1)
integral of (x+2)/(x^2+4x+5)	\int\:\frac{x+2}{x^{2}+4x+5}dx
integral of (e^{sqrt(x)+666})/(sqrt(x))	\int\:\frac{e^{\sqrt{x}+666}}{\sqrt{x}}dx
integral of 5x*sqrt(16-x^2)	\int\:5x\cdot\:\sqrt{16-x^{2}}dx
(\partial)/(\partial y)(2xy^4+3)	\frac{\partial\:}{\partial\:y}(2xy^{4}+3)
limit as x approaches 3-of (ln(x))/(x-3)	\lim\:_{x\to\:3-}(\frac{\ln(x)}{x-3})
(\partial)/(\partial x)(-sin(y)+e^x)	\frac{\partial\:}{\partial\:x}(-\sin(y)+e^{x})
derivative of x*tan(x)	\frac{d}{dx}(x\cdot\:\tan(x))
integral of 5/((3x-1)^3)	\int\:\frac{5}{(3x-1)^{3}}dx
integral of (e^{-5x}+3xe^x)/2	\int\:\frac{e^{-5x}+3xe^{x}}{2}dx
limit as x approaches+3 of 1/((x-3))	\lim\:_{x\to\:+3}(\frac{1}{(x-3)})
derivative of y=2(12x-42)	derivative\:y=2(12x-42)
laplacetransform 2t-8/3	laplacetransform\:2t-\frac{8}{3}
limit as z approaches 0 of (Im(z))/z	\lim\:_{z\to\:0}(\frac{Im(z)}{z})
taylor 2/x ,4	taylor\:\frac{2}{x},4
area y=4x^2,y=6x^2,5x+y=6>= 0	area\:y=4x^{2},y=6x^{2},5x+y=6\ge\:0
integral of 1/(\sqrt[3]{x^5)}	\int\:\frac{1}{\sqrt[3]{x^{5}}}dx
integral of e^{3x+8}	\int\:e^{3x+8}dx
derivative of (cot(x)/(1+csc(x)))	\frac{d}{dx}(\frac{\cot(x)}{1+\csc(x)})
(\partial)/(\partial y)(x^2+2y+2z)	\frac{\partial\:}{\partial\:y}(x^{2}+2y+2z)
c^'	c^{\prime\:}
(d^4)/(dx^4)(3x^4)	\frac{d^{4}}{dx^{4}}(3x^{4})
derivative of 4/(x+1)	derivative\:\frac{4}{x+1}
integral of (12sqrt(x)+sqrt(2))	\int\:(12\sqrt{x}+\sqrt{2})dx
(\partial)/(\partial x)(e^{9xz})	\frac{\partial\:}{\partial\:x}(e^{9xz})
integral of cos^4(x)+sin^4(x)	\int\:\cos^{4}(x)+\sin^{4}(x)dx
integral of tan^2(xse)c^4x	\int\:\tan^{2}(xse)c^{4}xdx
limit as x approaches 2 of (x^2)/(x^2+4)	\lim\:_{x\to\:2}(\frac{x^{2}}{x^{2}+4})
integral of cos(x)+1/8 x	\int\:\cos(x)+\frac{1}{8}xdx
derivative of-4sin(2x)	derivative\:-4\sin(2x)

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