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Popular Calculus Problems

integral of (5x^3)/(sqrt(49-x^2))	\int\:\frac{5x^{3}}{\sqrt{49-x^{2}}}dx
integral of (-2x+4)/(x^4-2x^3+2x^2-2x+1)	\int\:\frac{-2x+4}{x^{4}-2x^{3}+2x^{2}-2x+1}dx
limit as x approaches 0 of sqrt(x+4)	\lim\:_{x\to\:0}(\sqrt{x+4})
limit as x approaches 0 of (e^{(-1)/x})/(x)	\lim\:_{x\to\:0}(\frac{e^{\frac{-1}{x}}}{x})
integral of z^2e^{-3z^3}	\int\:z^{2}e^{-3z^{3}}dz
integral from-5 to 5 of (sqrt(25-x^2))^2	\int\:_{-5}^{5}(\sqrt{25-x^{2}})^{2}dx
derivative of cos(5x*5)	\frac{d}{dx}(\cos(5x)\cdot\:5)
derivative of (2e^x)^2-(10e^x)	derivative\:(2e^{x})^{2}-(10e^{x})
integral of 1/(7x^3)	\int\:\frac{1}{7x^{3}}dx
derivative of (7x+sqrt(x^2+3)^6)	\frac{d}{dx}((7x+\sqrt{x^{2}+3})^{6})
parity (sin^5(e^{2x}))/(cos(7^{6x))}	parity\:\frac{\sin^{5}(e^{2x})}{\cos(7^{6x})}
integral of 2x-3x^2	\int\:2x-3x^{2}dx
d/(dt)(cos(7t))	\frac{d}{dt}(\cos(7t))
integral of (2x^2+4)/((x^2-2x+2)^2)	\int\:\frac{2x^{2}+4}{(x^{2}-2x+2)^{2}}dx
(\partial)/(\partial x)(x^4-yx^2+2y^3)	\frac{\partial\:}{\partial\:x}(x^{4}-yx^{2}+2y^{3})
(dy)/(dx)=3y+4	\frac{dy}{dx}=3y+4
integral of cos^4(7x+2)	\int\:\cos^{4}(7x+2)dx
tangent of y=6e^x+x,(0,6)	tangent\:y=6e^{x}+x,(0,6)
(\partial)/(\partial x)(e^z+1/x+xe^{-y})	\frac{\partial\:}{\partial\:x}(e^{z}+\frac{1}{x}+xe^{-y})
integral of 2^5	\int\:2^{5}dx
(dy}{dx}=\frac{4sqrt(y)ln(x))/x ,y(e)=1	\frac{dy}{dx}=\frac{4\sqrt{y}\ln(x)}{x},y(e)=1
limit as x approaches-2 of x^3+x-1	\lim\:_{x\to\:-2}(x^{3}+x-1)
derivative of 7/(x+1)	\frac{d}{dx}(\frac{7}{x+1})
derivative of x^2ln(x/4)	\frac{d}{dx}(x^{2}\ln(\frac{x}{4}))
derivative of 6x^4(x^2-7x)	\frac{d}{dx}(6x^{4}(x^{2}-7x))
integral from 0 to pi/2 of 17cos^5(x)	\int\:_{0}^{\frac{π}{2}}17\cos^{5}(x)dx
integral of (2x)/(x^2-3x-10)	\int\:\frac{2x}{x^{2}-3x-10}dx
(\partial)/(\partial y)(x^{1/2}*y^{1/2})	\frac{\partial\:}{\partial\:y}(x^{\frac{1}{2}}\cdot\:y^{\frac{1}{2}})
d/(dt)((cos(t))/(sin(t)))	\frac{d}{dt}(\frac{\cos(t)}{\sin(t)})
derivative of xarctan(2x)	\frac{d}{dx}(x\arctan(2x))
limit as x approaches 0-of xcsc(x)	\lim\:_{x\to\:0-}(x\csc(x))
(d^2)/(dx^2)(cos(-2x))	\frac{d^{2}}{dx^{2}}(\cos(-2x))
derivative of cos(x^2+pi)	\frac{d}{dx}(\cos(x^{2}+π))
derivative of g(t)=sqrt(2)^t	derivative\:g(t)=\sqrt{2}^{t}
taylor x^2e^{x-1},\at 1	taylor\:x^{2}e^{x-1},\at\:1
integral of cot(19x)	\int\:\cot(19x)dx
integral of x^2(3x^3-2)^4	\int\:x^{2}(3x^{3}-2)^{4}dx
derivative of k^x+x^k	\frac{d}{dx}(k^{x}+x^{k})
integral from 0 to 2 of 2pi(x+1)(12-6x)	\int\:_{0}^{2}2π(x+1)(12-6x)dx
derivative of g(x)=3^{(x/2)}	derivative\:g(x)=3^{(\frac{x}{2})}
limit as x approaches 2 of ((3))/(x-2)	\lim\:_{x\to\:2}(\frac{(3)}{x-2})
integral of sec^7(3x)tan(3x)	\int\:\sec^{7}(3x)\tan(3x)dx
limit as x approaches 0-of cot(x)	\lim\:_{x\to\:0-}(\cot(x))
(x(csc(y/x))-y)dx+xdy=0	(x(\csc(\frac{y}{x}))-y)dx+xdy=0
derivative of f(x)=(2x)^3	derivative\:f(x)=(2x)^{3}
tangent of y= 1/((x-1))	tangent\:y=\frac{1}{(x-1)}
(\partial)/(\partial x)(1/(x^2)+y)	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}}+y)
(\partial)/(\partial y)(y^2)	\frac{\partial\:}{\partial\:y}(y^{2})
y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=4	y^{\prime\:\prime\:}+y^{\prime\:}-2y=2t,y(0)=0,y^{\prime\:}(0)=4
(\partial)/(\partial x)(sin(x)cosh(y))	\frac{\partial\:}{\partial\:x}(\sin(x)\cosh(y))
(dy)/(dx)=1+x+y+x*y	\frac{dy}{dx}=1+x+y+x\cdot\:y
limit as x approaches infinity of (1+5/x)^{x/7}	\lim\:_{x\to\:\infty\:}((1+\frac{5}{x})^{\frac{x}{7}})
integral of (2000)/(5x+10)	\int\:\frac{2000}{5x+10}dx
integral from 0 to 2 of xsqrt(5-x^2)	\int\:_{0}^{2}x\sqrt{5-x^{2}}dx
inverse oflaplace ((s+2))/((s^2+s+1))	inverselaplace\:\frac{(s+2)}{(s^{2}+s+1)}
inverse oflaplace (-25)/(s^2+6s+25)	inverselaplace\:\frac{-25}{s^{2}+6s+25}
tangent of f(x)=x^2-8,\at x=4	tangent\:f(x)=x^{2}-8,\at\:x=4
xy^'=3y-6x^2	xy^{\prime\:}=3y-6x^{2}
integral of cos(pix)cos(4pix)	\int\:\cos(πx)\cos(4πx)dx
area 3x,3, 3/x	area\:3x,3,\frac{3}{x}
integral of x/(2ln(x))	\int\:\frac{x}{2\ln(x)}dx
limit as x approaches 1 of x+2	\lim\:_{x\to\:1}(x+2)
limit as x approaches pi of ln(cos(x)-7)	\lim\:_{x\to\:π}(\ln(\cos(x)-7))
f(x)= 1/(3x^{2/3)}	f(x)=\frac{1}{3x^{\frac{2}{3}}}
integral of x^5sqrt(1+x^2)	\int\:x^{5}\sqrt{1+x^{2}}dx
y^{''}=ky	y^{\prime\:\prime\:}=ky
integral of (x^3)/(sqrt(x^2+16))	\int\:\frac{x^{3}}{\sqrt{x^{2}+16}}dx
derivative of \sqrt[4]{x^3}	derivative\:\sqrt[4]{x^{3}}
sum from n=1 to infinity of ((x^n))/(n!)	\sum\:_{n=1}^{\infty\:}\frac{(x^{n})}{n!}
derivative of sin^2(1-s^2)	derivative\:\sin^{2}(1-s^{2})
integral of tan^2(θ)sec^4(θ)	\int\:\tan^{2}(θ)\sec^{4}(θ)dθ
area x^3-3x,x	area\:x^{3}-3x,x
derivative of ln\|4x-3\|	\frac{d}{dx}(\ln\left\|4x-3\right\|)
integral of x(sqrt(2x-1))	\int\:x(\sqrt{2x-1})dx
limit as x approaches pi of ln\|cos(x)-8\|	\lim\:_{x\to\:π}(\ln\left\|\cos(x)-8\right\|)
integral of e^{-kx}	\int\:e^{-kx}dx
d/(dt)(e^t)	\frac{d}{dt}(e^{t})
limit as x approaches infinity of 3x-5	\lim\:_{x\to\:\infty\:}(3x-5)
limit as x approaches 0+of 1/(cos(x)-1)	\lim\:_{x\to\:0+}(\frac{1}{\cos(x)-1})
integral of x^2*sec^2(x^3)	\int\:x^{2}\cdot\:\sec^{2}(x^{3})dx
limit as x approaches 0 of (x^3-0)/x	\lim\:_{x\to\:0}(\frac{x^{3}-0}{x})
sum from n=1 to infinity of ne^{-3n}	\sum\:_{n=1}^{\infty\:}ne^{-3n}
limit as x approaches pi/2 of (1-tan(2x))/(2tan(x))	\lim\:_{x\to\:\frac{π}{2}}(\frac{1-\tan(2x)}{2\tan(x)})
derivative of x^{-8cos(x)}	derivative\:x^{-8\cos(x)}
derivative of 4x^2cos(2x)	\frac{d}{dx}(4x^{2}\cos(2x))
(dy)/(dx)=x+y-1	\frac{dy}{dx}=x+y-1
inverse oflaplace (-2e^{-2s})/((s^2-2s+1))	inverselaplace\:\frac{-2e^{-2s}}{(s^{2}-2s+1)}
inverse oflaplace 1/(s^3(s+4))	inverselaplace\:\frac{1}{s^{3}(s+4)}
derivative of 10x^{10}e^x	\frac{d}{dx}(10x^{10}e^{x})
integral of 1/(sqrt(-t^2+8t-15))	\int\:\frac{1}{\sqrt{-t^{2}+8t-15}}dt
derivative of x+e^x-1/x	derivative\:x+e^{x}-\frac{1}{x}
integral of ((4x-5))/((x-2)(x+3))	\int\:\frac{(4x-5)}{(x-2)(x+3)}dx
integral of y/(x(x+y))	\int\:\frac{y}{x(x+y)}dx
xy^'+y=e^x,y(1)=6	xy^{\prime\:}+y=e^{x},y(1)=6
integral of 9/(6+9x)	\int\:\frac{9}{6+9x}dx
integral of (2^x+e^pi)	\int\:(2^{x}+e^{π})dx
derivative of e^7	derivative\:e^{7}
dx+e^3xdy=0	dx+e^{3}xdy=0
tangent of f(x)=x^2,(-1,-3)	tangent\:f(x)=x^{2},(-1,-3)
area x^2-4x,x	area\:x^{2}-4x,x

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