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Popular Calculus Problems

integral of (y^5)/((1-y^3)^{3/2)}	\int\:\frac{y^{5}}{(1-y^{3})^{\frac{3}{2}}}dy
integral of 3x^3-xsqrt(x^4)+5e^x+3x^{1/3}-x-\sqrt[4]{x}+54	\int\:3x^{3}-x\sqrt{x^{4}}+5e^{x}+3x^{\frac{1}{3}}-x-\sqrt[4]{x}+54dx
derivative of f(x)=(x+x^4)(-x-1)	derivative\:f(x)=(x+x^{4})(-x-1)
y^'sin(2pix)=piycos(2pix)	y^{\prime\:}\sin(2πx)=πy\cos(2πx)
limit as x approaches 1-of 4-x-x^2	\lim\:_{x\to\:1-}(4-x-x^{2})
inverse oflaplace 4/(s^3)	inverselaplace\:\frac{4}{s^{3}}
integral of xsin(7-x)	\int\:x\sin(7-x)dx
(dx)/(dt)=x^2-3	\frac{dx}{dt}=x^{2}-3
integral of x^3sqrt(144-x^2)	\int\:x^{3}\sqrt{144-x^{2}}dx
derivative of-3x^2+6x	\frac{d}{dx}(-3x^{2}+6x)
tangent of xe^{3x}(2+3x)	tangent\:xe^{3x}(2+3x)
derivative of f(x)=x^{11}arccos(x)	derivative\:f(x)=x^{11}\arccos(x)
(\partial)/(\partial y)(sin(y)+ysin(x))	\frac{\partial\:}{\partial\:y}(\sin(y)+y\sin(x))
limit as x approaches 5-of 3	\lim\:_{x\to\:5-}(3)
y^{''}=x^2-1	y^{\prime\:\prime\:}=x^{2}-1
derivative of 5^{sqrt(x)}	derivative\:5^{\sqrt{x}}
integral of sqrt(3x-4)	\int\:\sqrt{3x-4}dx
limit as x approaches-1 of (x-2)/(x^2-1)	\lim\:_{x\to\:-1}(\frac{x-2}{x^{2}-1})
integral of 1/(u^2+1)	\int\:\frac{1}{u^{2}+1}du
(dy)/(dx)= 1/(sqrt(x))	\frac{dy}{dx}=\frac{1}{\sqrt{x}}
integral from 0 to 1 of (e^{x^2})	\int\:_{0}^{1}(e^{x^{2}})dx
x/y (dy)/(dx)+ln(y)=x+1	\frac{x}{y}\frac{dy}{dx}+\ln(y)=x+1
integral of 3/4 x^4	\int\:\frac{3}{4}x^{4}dx
limit as x approaches 2+of (2x+1)/(x-2)	\lim\:_{x\to\:2+}(\frac{2x+1}{x-2})
derivative of cos(x^5)	derivative\:\cos(x^{5})
sum from n=0 to infinity of (pi/e)^n	\sum\:_{n=0}^{\infty\:}(\frac{π}{e})^{n}
inverse oflaplace (e^{-2x})/(2x^2+1)	inverselaplace\:\frac{e^{-2x}}{2x^{2}+1}
y^{''}-3y^'-10y=4e^{4t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-3y^{\prime\:}-10y=4e^{4t},y(0)=0,y^{\prime\:}(0)=0
limit as x approaches-3 of 2x^2+4x+1	\lim\:_{x\to\:-3}(2x^{2}+4x+1)
sum from n=9 to infinity of e^{5-6n}	\sum\:_{n=9}^{\infty\:}e^{5-6n}
integral of (1/(1+9x^2))	\int\:(\frac{1}{1+9x^{2}})dx
derivative of 5sin(-4x)	\frac{d}{dx}(5\sin(-4x))
integral from 0 to 1 of-12x^2(4x^3-1)^3	\int\:_{0}^{1}-12x^{2}(4x^{3}-1)^{3}dx
taylor 1/(1+e^{x^2)}	taylor\:\frac{1}{1+e^{x^{2}}}
integral of 1/(sqrt(25-36x^2))	\int\:\frac{1}{\sqrt{25-36x^{2}}}dx
integral of 13tan^2(x)sec^3(x)	\int\:13\tan^{2}(x)\sec^{3}(x)dx
integral of-2x^2+8x	\int\:-2x^{2}+8xdx
y^{''}-3y^'+y=0	y^{\prime\:\prime\:}-3y^{\prime\:}+y=0
tangent of y=3x^3-3x	tangent\:y=3x^{3}-3x
(dy)/(dx)=5e^x	\frac{dy}{dx}=5e^{x}
derivative of ln(1+cos(x))	\frac{d}{dx}(\ln(1+\cos(x)))
integral from 0 to 1 of xarcsin(x^2)	\int\:_{0}^{1}x\arcsin(x^{2})dx
derivative of 1200sqrt(x^2-0.1x)	\frac{d}{dx}(1200\sqrt{x^{2}-0.1x})
derivative of 1/(x^3+1)	\frac{d}{dx}(\frac{1}{x^{3}+1})
(dy)/(dx)=xy+4x+5y+20	\frac{dy}{dx}=xy+4x+5y+20
integral of ((x-2)(x+2))/(x^2)	\int\:\frac{(x-2)(x+2)}{x^{2}}dx
integral from 0 to 2 of 3/(sqrt(16-x^2))	\int\:_{0}^{2}\frac{3}{\sqrt{16-x^{2}}}dx
derivative of (cos(x)^{pi/5})	\frac{d}{dx}((\cos(x))^{\frac{π}{5}})
integral from-2 to 3 of (45)/(x^4)	\int\:_{-2}^{3}\frac{45}{x^{4}}dx
(dy)/(dx)=(x+y)/(x+y+2)	\frac{dy}{dx}=\frac{x+y}{x+y+2}
integral of (x+5)/(x^2(x-2))	\int\:\frac{x+5}{x^{2}(x-2)}dx
limit as x approaches 0 of ln(1)	\lim\:_{x\to\:0}(\ln(1))
simplify e^{-4x}(cos(3x))	simplify\:e^{-4x}(\cos(3x))
derivative of csc^2(tan(2t))	derivative\:\csc^{2}(\tan(2t))
derivative of x^my^n	\frac{d}{dx}(x^{m}y^{n})
slope ofintercept (6,-9),(-2,-1)	slopeintercept\:(6,-9),(-2,-1)
2xy+x^2y^'=y^2	2xy+x^{2}y^{\prime\:}=y^{2}
integral of y^2(7-y^3)^{2/3}	\int\:y^{2}(7-y^{3})^{\frac{2}{3}}dy
derivative of 9(x^2+5x)^2(2x+5)	derivative\:9(x^{2}+5x)^{2}(2x+5)
derivative of y=(16)/x	derivative\:y=\frac{16}{x}
derivative of (7^x)^4	derivative\:(7^{x})^{4}
derivative of y(θ)=etan(θ)	derivative\:y(θ)=e\tan(θ)
(dy)/(dx)-3y=-6	\frac{dy}{dx}-3y=-6
integral from-infinity to 0 of 7^x	\int\:_{-\infty\:}^{0}7^{x}dx
f(x)=(sqrt(x)+1/(\sqrt[3]{x)})^2	f(x)=(\sqrt{x}+\frac{1}{\sqrt[3]{x}})^{2}
laplacetransform e^{2t}t^3	laplacetransform\:e^{2t}t^{3}
integral of 2/(x^3sqrt(x^2-1))	\int\:\frac{2}{x^{3}\sqrt{x^{2}-1}}dx
integral of (2x-y)	\int\:(2x-y)dx
(\partial)/(\partial y)(y^2x)	\frac{\partial\:}{\partial\:y}(y^{2}x)
derivative of 0.00037x^2	\frac{d}{dx}(0.00037x^{2})
maclaurin ln(1+5x)	maclaurin\:\ln(1+5x)
integral from 0 to 1 of xsqrt(1-x^4)	\int\:_{0}^{1}x\sqrt{1-x^{4}}dx
integral of sqrt(x)sqrt(x^{3/2)-1}	\int\:\sqrt{x}\sqrt{x^{\frac{3}{2}}-1}dx
derivative of log_{5}(2x^2+1)	\frac{d}{dx}(\log_{5}(2x^{2}+1))
(2x+2/y)+(((2x^2))/y+(2x)/(y^2))y^'=0	(2x+\frac{2}{y})+(\frac{(2x^{2})}{y}+\frac{2x}{y^{2}})y^{\prime\:}=0
tangent of f(x)=x^4-10x^2+9	tangent\:f(x)=x^{4}-10x^{2}+9
integral of-(14)/(x^{15)}	\int\:-\frac{14}{x^{15}}dx
integral of x^n	\int\:x^{n}dx
derivative of 3x^2+1/(x^3)	\frac{d}{dx}(3x^{2}+\frac{1}{x^{3}})
limit as x approaches 0-of sin(1/x)	\lim\:_{x\to\:0-}(\sin(\frac{1}{x}))
derivative of e^x(3x^2+5x-1)	\frac{d}{dx}(e^{x}(3x^{2}+5x-1))
integral of 1-2cos(2x)	\int\:1-2\cos(2x)dx
integral of 1/(2x^2sqrt(x^2-9))	\int\:\frac{1}{2x^{2}\sqrt{x^{2}-9}}dx
tangent of f(x)=(5x-5)^{1/4},\at x=2	tangent\:f(x)=(5x-5)^{\frac{1}{4}},\at\:x=2
derivative of 4sin(x-5cos(x)+x)	\frac{d}{dx}(4\sin(x)-5\cos(x)+x)
derivative of y^{-2}	derivative\:y^{-2}
limit as x approaches 1 of x-1/(ln\|x\|)	\lim\:_{x\to\:1}(x-\frac{1}{\ln\left\|x\right\|})
6x^2y^'=y^'+8xe^{-y}	6x^{2}y^{\prime\:}=y^{\prime\:}+8xe^{-y}
f(t)=(\sqrt[3]{t})/(t-9)	f(t)=\frac{\sqrt[3]{t}}{t-9}
integral of (4x^2+4x-4)/(x^3+x^2-x-1)	\int\:\frac{4x^{2}+4x-4}{x^{3}+x^{2}-x-1}dx
(\partial)/(\partial y)(2xz^3e^{y^2})	\frac{\partial\:}{\partial\:y}(2xz^{3}e^{y^{2}})
tangent of sqrt(x),\at x=1	tangent\:\sqrt{x},\at\:x=1
integral of x(sqrt(x)-3)	\int\:x(\sqrt{x}-3)dx
derivative of 3-3x^2	\frac{d}{dx}(3-3x^{2})
derivative of f(x)=-7/((x+4)^2)	derivative\:f(x)=-\frac{7}{(x+4)^{2}}
laplacetransform f(t)=(1)(t^3)	laplacetransform\:f(t)=(1)(t^{3})
derivative of 1/(16x^4)	\frac{d}{dx}(\frac{1}{16x^{4}})
-3y^'+(3y)/x =xy^4	-3y^{\prime\:}+\frac{3y}{x}=xy^{4}
integral of x/((x^2-3)^3)	\int\:\frac{x}{(x^{2}-3)^{3}}dx
integral of (4sin(5x)+5cos(3x))	\int\:(4\sin(5x)+5\cos(3x))dx

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