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Popular Calculus Problems

integral of (x+4)/(x^2+16)	\int\:\frac{x+4}{x^{2}+16}dx
y^{''}-5y^'+6y=e^t	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=e^{t}
integral from 0 to 1 of sqrt(9t^4+4t^2)	\int\:_{0}^{1}\sqrt{9t^{4}+4t^{2}}dt
integral from 1 to 4 of (x^2+x)	\int\:_{1}^{4}(x^{2}+x)dx
derivative of-x^{-2}	\frac{d}{dx}(-x^{-2})
integral of sqrt(e^x-1)	\int\:\sqrt{e^{x}-1}dx
derivative of x^4-8x^2	\frac{d}{dx}(x^{4}-8x^{2})
integral from 1 to e^3 of (ln^4(x^2))/x	\int\:_{1}^{e^{3}}\frac{\ln^{4}(x^{2})}{x}dx
derivative of 3^{sin(x})	\frac{d}{dx}(3^{\sin(x)})
derivative of tan(sqrt(5x))	\frac{d}{dx}(\tan(\sqrt{5x}))
limit as x approaches 1 of 3x^3-5x^2+5	\lim\:_{x\to\:1}(3x^{3}-5x^{2}+5)
integral of (x^2)/(4x^2+1)	\int\:\frac{x^{2}}{4x^{2}+1}dx
derivative of 7e^{1-x^2}	derivative\:7e^{1-x^{2}}
integral of ((1+x)/x)^3	\int\:(\frac{1+x}{x})^{3}dx
derivative of ((sqrt(x)-2))/(sqrt(x)+2)	derivative\:\frac{(\sqrt{x}-2)}{\sqrt{x}+2}
integral of sin^8(x)cos^5(x)	\int\:\sin^{8}(x)\cos^{5}(x)dx
derivative of (e^x/(-8x^7))	\frac{d}{dx}(\frac{e^{x}}{-8x^{7}})
limit as x approaches-infinity of 5x^5-7x^4+1	\lim\:_{x\to\:-\infty\:}(5x^{5}-7x^{4}+1)
xcos^2(y)dx+tan(y)dy=0	x\cos^{2}(y)dx+\tan(y)dy=0
slope ofintercept (1.1)(0.1)	slopeintercept\:(1.1)(0.1)
derivative of tan(2x^5)	\frac{d}{dx}(\tan(2x^{5}))
integral of (2x)/(x^2-x-2)	\int\:\frac{2x}{x^{2}-x-2}dx
limit as s approaches 0 of 1/(s^20.1s+1)	\lim\:_{s\to\:0}(\frac{1}{s^{2}0.1s+1})
integral of 4cos^2(t)	\int\:4\cos^{2}(t)dt
limit as x approaches 0 of (sin^2(6x))/x	\lim\:_{x\to\:0}(\frac{\sin^{2}(6x)}{x})
limit as x approaches infinity of 2x^x	\lim\:_{x\to\:\infty\:}(2x^{x})
y^{''}+3y^'=0,y(0)=9,y^'(0)=-6	y^{\prime\:\prime\:}+3y^{\prime\:}=0,y(0)=9,y^{\prime\:}(0)=-6
sum from n=1 to infinity of n(1-p)^{n-1}	\sum\:_{n=1}^{\infty\:}n(1-p)^{n-1}
area 9x,x^2-10,0	area\:9x,x^{2}-10,0
integral of e^{6x}x^3	\int\:e^{6x}x^{3}dx
derivative of y=ln(sqrt((x+3)/(x-3)))	derivative\:y=\ln(\sqrt{\frac{x+3}{x-3}})
(\partial)/(\partial x)(y^6-5xy)	\frac{\partial\:}{\partial\:x}(y^{6}-5xy)
integral of sqrt(1+x^2)	\int\:\sqrt{1+x^{2}}dx
(\partial)/(\partial z)(1/(xyz^2))	\frac{\partial\:}{\partial\:z}(\frac{1}{xyz^{2}})
(dy}{dx}=\frac{-xy^2)/2	\frac{dy}{dx}=\frac{-xy^{2}}{2}
limit as x approaches 2 of (x-2)(2^x-4)	\lim\:_{x\to\:2}((x-2)(2^{x}-4))
derivative of x^{3^x}	derivative\:x^{3^{x}}
integral of ((x+2)^2)/(x^2+4)	\int\:\frac{(x+2)^{2}}{x^{2}+4}dx
integral of (x+66)/(x^2-36)	\int\:\frac{x+66}{x^{2}-36}dx
integral of (3x-4)^2	\int\:(3x-4)^{2}dx
derivative of csc(x^3)	\frac{d}{dx}(\csc(x^{3}))
derivative of f(x)=(8x^2-x+5)/(x+5)	derivative\:f(x)=\frac{8x^{2}-x+5}{x+5}
d/(dy)(sin(xy^2))	\frac{d}{dy}(\sin(xy^{2}))
integral of 6sin(2x)+sec^2(x)	\int\:6\sin(2x)+\sec^{2}(x)dx
integral of e^{13x}(13)	\int\:e^{13x}(13)dx
integral of 16cos^2(t)	\int\:16\cos^{2}(t)dt
limit as x approaches 3 of x/(3-x)	\lim\:_{x\to\:3}(\frac{x}{3-x})
f(x)=5x-3	f(x)=5x-3
integral of (x+5)	\int\:(x+5)dx
derivative of (x^3+6/x)	\frac{d}{dx}(\frac{x^{3}+6}{x})
derivative of (8+x/(1-8x))	\frac{d}{dx}(\frac{8+x}{1-8x})
integral of 19sin^3(xco)s^2x	\int\:19\sin^{3}(xco)s^{2}xdx
tangent of y=x^2+x,(-1,0)	tangent\:y=x^{2}+x,(-1,0)
derivative of (x^2/((x^2-1)^4))	\frac{d}{dx}(\frac{x^{2}}{(x^{2}-1)^{4}})
f(x)=(t^3)/6-2/(t^2)	f(x)=\frac{t^{3}}{6}-\frac{2}{t^{2}}
t^2y^{''}+19ty^'+90y=0	t^{2}y^{\prime\:\prime\:}+19ty^{\prime\:}+90y=0
-2y^{''}+8y=0	-2y^{\prime\:\prime\:}+8y=0
derivative of e^{t/9}	derivative\:e^{\frac{t}{9}}
derivative of f(x)=(3x^2-2x+1)^{1/2}	derivative\:f(x)=(3x^{2}-2x+1)^{\frac{1}{2}}
integral of 4cos((npix)/4)	\int\:4\cos(\frac{nπx}{4})dx
inverse oflaplace x/(x^2+0.0184)	inverselaplace\:\frac{x}{x^{2}+0.0184}
limit as x approaches-4pi of sqrt(x+15)cos(x+4pi)	\lim\:_{x\to\:-4π}(\sqrt{x+15}\cos(x+4π))
limit as x approaches-4 of 8x+1	\lim\:_{x\to\:-4}(8x+1)
integral of x^4e^{8x^5}	\int\:x^{4}e^{8x^{5}}dx
derivative of f(x)=e^3	derivative\:f(x)=e^{3}
tangent of f(x)=x^5,(1,1)	tangent\:f(x)=x^{5},(1,1)
derivative of sec(xtan(y))	\frac{d}{dx}(\sec(x)\tan(y))
integral of 81-x^2	\int\:81-x^{2}dx
derivative of 3+x^{10}e^x	\frac{d}{dx}(3+x^{10}e^{x})
integral of 1/(2^2+2x^2)	\int\:\frac{1}{2^{2}+2x^{2}}dx
(dy)/(dx)=4xe^{(3y)}	\frac{dy}{dx}=4xe^{(3y)}
integral of ((x+3)^2)/(sqrt(x))	\int\:\frac{(x+3)^{2}}{\sqrt{x}}dx
integral of-1280(1+4x)^{-3}	\int\:-1280(1+4x)^{-3}dx
derivative of (x^2-4/x)	\frac{d}{dx}(\frac{x^{2}-4}{x})
integral of (x^4-1)/(x^2+1)	\int\:\frac{x^{4}-1}{x^{2}+1}dx
integral of (sec^2(x)-4)	\int\:(\sec^{2}(x)-4)dx
taylor x^{-2},4	taylor\:x^{-2},4
integral of 5/(4x)	\int\:\frac{5}{4x}dx
integral of e^{-x-1}	\int\:e^{-x-1}dx
(\partial)/(\partial x)(sin(2x+5y))	\frac{\partial\:}{\partial\:x}(\sin(2x+5y))
integral of (tan^4(x))	\int\:(\tan^{4}(x))dx
integral of (pix^3+1)^43pix^2	\int\:(πx^{3}+1)^{4}3πx^{2}dx
(\partial)/(\partial x)(sqrt(10-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{10-x^{2}-y^{2}})
(\partial)/(\partial x)(ln(8-xe^{-x}))	\frac{\partial\:}{\partial\:x}(\ln(8-xe^{-x}))
derivative of ((4x^2/(8-x))^3)	\frac{d}{dx}((\frac{4x^{2}}{8-x})^{3})
limit as x approaches 1 of (x^3+1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{3}+1}{x-1})
(\partial)/(\partial y)((y^2)/(x+1))	\frac{\partial\:}{\partial\:y}(\frac{y^{2}}{x+1})
derivative of 3sin(θ)	derivative\:3\sin(θ)
inverse oflaplace f(s)= 2/((4s^2-8s))	inverselaplace\:f(s)=\frac{2}{(4s^{2}-8s)}
(\partial)/(\partial x)(x^{0.6}*y^{0.4})	\frac{\partial\:}{\partial\:x}(x^{0.6}\cdot\:y^{0.4})
integral of 4x(x^2+30000)^{-2/3}	\int\:4x(x^{2}+30000)^{-\frac{2}{3}}dx
integral of-2/x	\int\:-\frac{2}{x}dx
tangent of f(x)=sqrt(2x),(2,2)	tangent\:f(x)=\sqrt{2x},(2,2)
inverse oflaplace 2/(s^2(s^2-2s+5))	inverselaplace\:\frac{2}{s^{2}(s^{2}-2s+5)}
integral of xcos(x^2+4)	\int\:x\cos(x^{2}+4)dx
tangent of y= 5/(sqrt(x))	tangent\:y=\frac{5}{\sqrt{x}}
derivative of e^{2x-2}	\frac{d}{dx}(e^{2x-2})
simplify x^2-16ln(x^2)	simplify\:x^{2}-16\ln(x^{2})
integral of 8xe^{7x}	\int\:8xe^{7x}dx
integral of sin(wx+pi/3)sin(wx)	\int\:\sin(wx+\frac{π}{3})\sin(wx)dx

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