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Popular Calculus Problems

integral of (1/(x*(5-x)))	\int\:(\frac{1}{x\cdot\:(5-x)})dx
maclaurin (1+x)^n	maclaurin\:(1+x)^{n}
integral of tan(3x)sec^2(3x)	\int\:\tan(3x)\sec^{2}(3x)dx
derivative of (40x^5/(e^x))	\frac{d}{dx}(\frac{40x^{5}}{e^{x}})
limit as x approaches 0+of 1+csc(x)	\lim\:_{x\to\:0+}(1+\csc(x))
derivative of 3sin(x-4cos(x))	\frac{d}{dx}(3\sin(x)-4\cos(x))
derivative of sqrt(2+\sqrt{x)}	\frac{d}{dx}(\sqrt{2+\sqrt{x}})
inverse oflaplace (e^{(-s)})/(s^2-4)	inverselaplace\:\frac{e^{(-s)}}{s^{2}-4}
derivative of (1+1/x ^3)	\frac{d}{dx}((1+\frac{1}{x})^{3})
integral of (-30)/((2x+1)^2)+30	\int\:\frac{-30}{(2x+1)^{2}}+30dx
(\partial)/(\partial x)((ln(x))^x)	\frac{\partial\:}{\partial\:x}((\ln(x))^{x})
integral of-8sin(sqrt(x))	\int\:-8\sin(\sqrt{x})dx
integral of-x^4+((9x^2))/4-2x+3	\int\:-x^{4}+\frac{(9x^{2})}{4}-2x+3dx
(2x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=5	(2x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0,y(1)=5
(\partial)/(\partial x)((1-y)+10(x-y^2)^2)	\frac{\partial\:}{\partial\:x}((1-y)+10(x-y^{2})^{2})
xy^'+3y=x^2-1	xy^{\prime\:}+3y=x^{2}-1
(\partial)/(\partial x)(x/y+y/x)	\frac{\partial\:}{\partial\:x}(\frac{x}{y}+\frac{y}{x})
expand (x+a)e^{3x}+b	expand\:(x+a)e^{3x}+b
2sqrt(x)(dy)/(dx)=sqrt(1-y^2)	2\sqrt{x}\frac{dy}{dx}=\sqrt{1-y^{2}}
integral from 0 to 1 of (e^x)	\int\:_{0}^{1}(e^{x})dx
integral of (sin^3(x))/(cos(x))	\int\:\frac{\sin^{3}(x)}{\cos(x)}dx
integral from 0 to 1 of te^{-t}	\int\:_{0}^{1}te^{-t}dt
inverse oflaplace 5/(s(s-1))	inverselaplace\:\frac{5}{s(s-1)}
limit as x approaches 2 of (x^2+3)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{2}+3}{x-2})
integral of (1+3x^2)ln(2x)	\int\:(1+3x^{2})\ln(2x)dx
tangent of f(x)=12sqrt(x)-2x	tangent\:f(x)=12\sqrt{x}-2x
x(dy)/(dx)=2y	x\frac{dy}{dx}=2y
laplacetransform t^2cos(-2t)	laplacetransform\:t^{2}\cos(-2t)
integral from 0 to 1 of 2/(1+x^2)	\int\:_{0}^{1}\frac{2}{1+x^{2}}dx
y^'= 1/(e^y-x)	y^{\prime\:}=\frac{1}{e^{y}-x}
derivative of 2x+2y	\frac{d}{dx}(2x+2y)
derivative of \|ln\|x\|\|	\frac{d}{dx}(\left\|\ln\left\|x\right\|\right\|)
derivative of 5/2	\frac{d}{dx}(\frac{5}{2})
(\partial)/(\partial x)(8xln(xy-7))	\frac{\partial\:}{\partial\:x}(8x\ln(xy-7))
derivative of 4arccos(-5x)	\frac{d}{dx}(4\arccos(-5x))
area 1,\sqrt[4]{x},0,1	area\:1,\sqrt[4]{x},0,1
d/(dθ)(2cos(θ)+4sin(θ))	\frac{d}{dθ}(2\cos(θ)+4\sin(θ))
derivative of (sin(x)^4+sin(x^4))	\frac{d}{dx}((\sin(x))^{4}+\sin(x^{4}))
inverse oflaplace 1/(4s+2)	inverselaplace\:\frac{1}{4s+2}
limit as x approaches-3 of-x^2+9x-1	\lim\:_{x\to\:-3}(-x^{2}+9x-1)
integral of 7/(sqrt(x^2+16))	\int\:\frac{7}{\sqrt{x^{2}+16}}dx
d/(dθ)(2θ)	\frac{d}{dθ}(2θ)
derivative of x^2tan(xy)	\frac{d}{dx}(x^{2}\tan(xy))
derivative of (3x+1/(7x+5))	\frac{d}{dx}(\frac{3x+1}{7x+5})
derivative of (x^x/(sin(x)))	\frac{d}{dx}(\frac{x^{x}}{\sin(x)})
roots asin(t/c)	roots\:a\sin(\frac{t}{c})
integral of x^{1/3}sin(x^{4/3}+8)	\int\:x^{\frac{1}{3}}\sin(x^{\frac{4}{3}}+8)dx
limit as x approaches 0+of 1/x-1/(e^x-1)	\lim\:_{x\to\:0+}(\frac{1}{x}-\frac{1}{e^{x}-1})
derivative of e^{cos(x-2sec(x)})	\frac{d}{dx}(e^{\cos(x)-2\sec(x)})
(d^3)/(dx^3)(-sin(3x))	\frac{d^{3}}{dx^{3}}(-\sin(3x))
integral of (ln(6x))^2	\int\:(\ln(6x))^{2}dx
(dy)/(dx)=k*y^2	\frac{dy}{dx}=k\cdot\:y^{2}
integral of sin^5(x)cos^7(x)	\int\:\sin^{5}(x)\cos^{7}(x)dx
(dy)/(dx)= 1/(1+x)	\frac{dy}{dx}=\frac{1}{1+x}
integral of sqrt(2m(E-1/2 kx^2))	\int\:\sqrt{2m(E-\frac{1}{2}kx^{2})}dx
derivative of f(x)=-12x^2+400x-3800	derivative\:f(x)=-12x^{2}+400x-3800
tangent of 3x-4x^2	tangent\:3x-4x^{2}
integral of (1-sin^2(x))cos(x)	\int\:(1-\sin^{2}(x))\cos(x)dx
derivative of (x^5-5/(x+1))	\frac{d}{dx}(\frac{x^{5}-5}{x+1})
(\partial)/(\partial x)(2x^2y+sin(x^4))	\frac{\partial\:}{\partial\:x}(2x^{2}y+\sin(x^{4}))
limit as x approaches 1 of x^{8/(1-x)}	\lim\:_{x\to\:1}(x^{\frac{8}{1-x}})
(\partial)/(\partial x)((x^3+y^3)^{1/3})	\frac{\partial\:}{\partial\:x}((x^{3}+y^{3})^{\frac{1}{3}})
integral of 1/(xsqrt(9-4x^2))	\int\:\frac{1}{x\sqrt{9-4x^{2}}}dx
integral of 2y-2	\int\:2y-2dy
integral from 0 to infinity of 5e^{-2x}	\int\:_{0}^{\infty\:}5e^{-2x}dx
integral of e^{-2x}tan(e^{-2x})	\int\:e^{-2x}\tan(e^{-2x})dx
y^{''}-y^'+y=cos(2t)+sin(2t)	y^{\prime\:\prime\:}-y^{\prime\:}+y=\cos(2t)+\sin(2t)
inverse oflaplace 1/(s(s^2+6pis+pi^2))	inverselaplace\:\frac{1}{s(s^{2}+6πs+π^{2})}
integral of (3tan(x)-4cos^2(x))/(cos(x))	\int\:\frac{3\tan(x)-4\cos^{2}(x)}{\cos(x)}dx
simplify 5x^2(3x^2-1)^2	simplify\:5x^{2}(3x^{2}-1)^{2}
integral of ((x-1)^5+3(x-1)^2+5)	\int\:((x-1)^{5}+3(x-1)^{2}+5)dx
(\partial)/(\partial x)(e^x(sin(y)-y))	\frac{\partial\:}{\partial\:x}(e^{x}(\sin(y)-y))
limit as x approaches+1+of sqrt(2x-2)-2	\lim\:_{x\to\:+1+}(\sqrt{2x-2}-2)
integral of 1/(x-7)	\int\:\frac{1}{x-7}dx
integral of (6x-5)/(3x^2+5)	\int\:\frac{6x-5}{3x^{2}+5}dx
y^'=(x^2y^4+2x^2)/(y^3)	y^{\prime\:}=\frac{x^{2}y^{4}+2x^{2}}{y^{3}}
integral of (1+e^{2x})/(e^x)	\int\:\frac{1+e^{2x}}{e^{x}}dx
y^'=-2xy	y^{\prime\:}=-2xy
(dy)/(dx)=cot(1-2x^2)	\frac{dy}{dx}=\cot(1-2x^{2})
integral of 1/(z^3sqrt(z^2-64))	\int\:\frac{1}{z^{3}\sqrt{z^{2}-64}}dz
integral of 9/(x+2)	\int\:\frac{9}{x+2}dx
limit as x approaches 4-of 3/(x-4)	\lim\:_{x\to\:4-}(\frac{3}{x-4})
derivative of (4x)/(sqrt(x^2+6))	derivative\:\frac{4x}{\sqrt{x^{2}+6}}
integral of 9sin^2(x)cos^3(x)	\int\:9\sin^{2}(x)\cos^{3}(x)dx
(\partial)/(\partial x)(cos(5z)e^{3x+4y}*3)	\frac{\partial\:}{\partial\:x}(\cos(5z)e^{3x+4y}\cdot\:3)
limit as x approaches 1-of xln(x)	\lim\:_{x\to\:1-}(x\ln(x))
y^'-(2x+1)y+3x(5x-2)=0	y^{\prime\:}-(2x+1)y+3x(5x-2)=0
taylor 5/x ,1	taylor\:\frac{5}{x},1
integral from 2 to 7 of 1/(sqrt(4x+8))	\int\:_{2}^{7}\frac{1}{\sqrt{4x+8}}dx
integral of (x+1)/((x+2)(x-3))	\int\:\frac{x+1}{(x+2)(x-3)}dx
integral of (tan(2x)+cot(2x))^2	\int\:(\tan(2x)+\cot(2x))^{2}dx
tangent of (6x)/((3-2x)^3)	tangent\:\frac{6x}{(3-2x)^{3}}
derivative of (6x+5^2)	\frac{d}{dx}((6x+5)^{2})
y^{''}+16y=24sin(4t)	y^{\prime\:\prime\:}+16y=24\sin(4t)
integral of ((x^2)/(x+1))	\int\:(\frac{x^{2}}{x+1})dx
f(x)=-3x	f(x)=-3x
integral of (sin(x)-cos(x))^2	\int\:(\sin(x)-\cos(x))^{2}dx
tangent of x^3-27x	tangent\:x^{3}-27x
x^2y^'-ysqrt(x)=0	x^{2}y^{\prime\:}-y\sqrt{x}=0
derivative of 6x^4-2x+7	\frac{d}{dx}(6x^{4}-2x+7)

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