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Popular Calculus Problems

derivative of f(x)=x+4	derivative\:f(x)=x+4
integral of (x^2-x+14)/(x^3+7x)	\int\:\frac{x^{2}-x+14}{x^{3}+7x}dx
derivative of f(x)=\sqrt[3]{1+8x}	derivative\:f(x)=\sqrt[3]{1+8x}
integral of (x^2+2x)/(sqrt(x^3+3x^2+2))	\int\:\frac{x^{2}+2x}{\sqrt{x^{3}+3x^{2}+2}}dx
y^{''}-y=t^2e^t	y^{\prime\:\prime\:}-y=t^{2}e^{t}
integral of (x^2)/(sqrt(x^3))	\int\:\frac{x^{2}}{\sqrt{x^{3}}}dx
(dy)/((6+y)^2)=(dx)/((10+9x)^4)	\frac{dy}{(6+y)^{2}}=\frac{dx}{(10+9x)^{4}}
(df)/(dθ)=sin(θ)+csc(θ)	\frac{df}{dθ}=\sin(θ)+\csc(θ)
integral of (2x^3-5x+7)	\int\:(2x^{3}-5x+7)dx
d/(dv)(sqrt(u*v))	\frac{d}{dv}(\sqrt{u\cdot\:v})
derivative of f(θ)=4sin(θ)-θ	derivative\:f(θ)=4\sin(θ)-θ
derivative of 4x^2cos(x)cot(x)	derivative\:4x^{2}\cos(x)\cot(x)
integral of e^{xyz}	\int\:e^{xyz}dx
limit as x approaches 1 of sin(3pix)	\lim\:_{x\to\:1}(\sin(3πx))
y+(x+1)(dy)/(dx)=2x+2,y(0)=2	y+(x+1)\frac{dy}{dx}=2x+2,y(0)=2
y^'=-8xy	y^{\prime\:}=-8xy
(dy)/(dx)=e^{2x-y}	\frac{dy}{dx}=e^{2x-y}
integral of-e^{-x}ln(x)	\int\:-e^{-x}\ln(x)dx
(1+x^2)(e^{2t}dt-e^xdx)-(1+x)dx=0	(1+x^{2})(e^{2t}dt-e^{x}dx)-(1+x)dx=0
inverse oflaplace (se^{-2s})/(s^2+16)	inverselaplace\:\frac{se^{-2s}}{s^{2}+16}
integral from 0 to 1 of cos^2(pix)	\int\:_{0}^{1}\cos^{2}(πx)dx
integral of (2-sqrt(x))/(x^2)	\int\:\frac{2-\sqrt{x}}{x^{2}}dx
d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2})	\frac{d}{d{y}}(({x}^{2}+{y}^{2}+{z}^{2})^{-\frac{1}{2}})
integral of 54-18z-6z^2+2z^3	\int\:54-18z-6z^{2}+2z^{3}dz
integral from 0 to 1 of 2x5^x	\int\:_{0}^{1}2x5^{x}dx
derivative of v^{3/2}(v+ce^x)	derivative\:v^{\frac{3}{2}}(v+ce^{x})
(y+xcos^2(y/x))dx-xdy=0	(y+x\cos^{2}(\frac{y}{x}))dx-xdy=0
integral of (6x)/(1+x^4)	\int\:\frac{6x}{1+x^{4}}dx
(dx)/(dt)=349.344897(1-e^{-0.0916t})	\frac{dx}{dt}=349.344897(1-e^{-0.0916t})
integral of (3e^{-0.4x})	\int\:(3e^{-0.4x})dx
integral of 4sin(x)-1+8x^{-5}	\int\:4\sin(x)-1+8x^{-5}dx
derivative of f(-3)=20x^4	derivative\:f(-3)=20x^{4}
integral of 3e^{4x+e^{4x}}	\int\:3e^{4x+e^{4x}}dx
derivative of (3-3x-x^2/(x^2-5))	\frac{d}{dx}(\frac{3-3x-x^{2}}{x^{2}-5})
integral of 1/(3-x)	\int\:\frac{1}{3-x}dx
integral from 1 to ln(x) of 1/x	\int\:_{1}^{\ln(x)}\frac{1}{x}dx
derivative of 3pi^4	\frac{d}{dx}(3π^{4})
integral of sqrt(10-4x-4x^2)	\int\:\sqrt{10-4x-4x^{2}}dx
(\partial)/(\partial z)(2e^xcos(yz))	\frac{\partial\:}{\partial\:z}(2e^{x}\cos(yz))
limit as x approaches 0 of x^2-x	\lim\:_{x\to\:0}(x^{2}-x)
derivative of (6x^{3x})	\frac{d}{dx}((6x)^{3x})
integral of sec(x)tan(x)	\int\:\sec(x)\tan(x)dx
y^{''}+5y^'=(4t-2)sin(2t)	y^{\prime\:\prime\:}+5y^{\prime\:}=(4t-2)\sin(2t)
d/(dt)(3te^t)	\frac{d}{dt}(3te^{t})
2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=24	2y^{\prime\:\prime\:}+5y^{\prime\:}-3y=0,y(0)=-1,y^{\prime\:}(0)=24
integral from-3 to-1 of (x+2)^{99}	\int\:_{-3}^{-1}(x+2)^{99}dx
derivative of 7sqrt(x)-9/(x^6)	derivative\:7\sqrt{x}-\frac{9}{x^{6}}
tangent of f(x)=xe^{-x/2},\at x= 1/2	tangent\:f(x)=xe^{-\frac{x}{2}},\at\:x=\frac{1}{2}
integral of (x^3)/(x^4-1)	\int\:\frac{x^{3}}{x^{4}-1}dx
t^2y^{''}+2ty^'-30y=0	t^{2}y^{\prime\:\prime\:}+2ty^{\prime\:}-30y=0
limit as x approaches 3 of ((x+3))/(x-3)	\lim\:_{x\to\:3}(\frac{(x+3)}{x-3})
integral of (ln(5x))^2	\int\:(\ln(5x))^{2}dx
integral of ((17x+3))/((4x+1)(x-1))	\int\:\frac{(17x+3)}{(4x+1)(x-1)}dx
limit as x approaches 0 of x^2ln(x)	\lim\:_{x\to\:0}(x^{2}\ln(x))
derivative of 1/(5sin(x)+(csc(x))/4)	\frac{d}{dx}(\frac{1}{5\sin(x)}+\frac{\csc(x)}{4})
derivative of x-sin^2(x-4xye^{xy^2})	\frac{d}{dx}(x-\sin^{2}(x)-4xye^{xy^{2}})
xy^'+4y=((2e^{-4x}))/(x^3)	xy^{\prime\:}+4y=\frac{(2e^{-4x})}{x^{3}}
derivative of (x+2/(x-1))	\frac{d}{dx}(\frac{x+2}{x-1})
3x^2y+(dy)/(dx)=4x^2	3x^{2}y+\frac{dy}{dx}=4x^{2}
integral of \sqrt[5]{x}+1/(\sqrt[5]{x)}	\int\:\sqrt[5]{x}+\frac{1}{\sqrt[5]{x}}dx
sum from n=0 to infinity of 3.25^n	\sum\:_{n=0}^{\infty\:}3.25^{n}
tangent of f(x)= 1/(3+2x),\at x=1	tangent\:f(x)=\frac{1}{3+2x},\at\:x=1
integral of (4x+2)	\int\:(4x+2)dx
derivative of ln(xsqrt(x^2+7))	derivative\:\ln(x\sqrt{x^{2}+7})
integral of ((cos(x)))/(sin(x))	\int\:\frac{(\cos(x))}{\sin(x)}dx
derivative of 1/t	derivative\:\frac{1}{t}
derivative of sqrt((x+1/(x-1)))	\frac{d}{dx}(\sqrt{\frac{x+1}{x-1}})
limit as x approaches 0+of 1+1/x	\lim\:_{x\to\:0+}(1+\frac{1}{x})
laplacetransform 5e^{-2(t-1)}	laplacetransform\:5e^{-2(t-1)}
sum from n=1 to infinity of (-3)^{-n}	\sum\:_{n=1}^{\infty\:}(-3)^{-n}
(\partial)/(\partial x)(4y)	\frac{\partial\:}{\partial\:x}(4y)
(\partial)/(\partial x)(6x+5y)	\frac{\partial\:}{\partial\:x}(6x+5y)
integral of x/((x+1)^4)	\int\:\frac{x}{(x+1)^{4}}dx
sum from n=1 to infinity of 3e^{-9n}	\sum\:_{n=1}^{\infty\:}3e^{-9n}
area f(x)= 1/(x^2),[2,6]	area\:f(x)=\frac{1}{x^{2}},[2,6]
tangent of (ln(x))^4	tangent\:(\ln(x))^{4}
integral of sqrt(2+e^{2x)+e^{-2x}}	\int\:\sqrt{2+e^{2x}+e^{-2x}}dx
(\partial)/(\partial y)(x^3-y^3+2xy)	\frac{\partial\:}{\partial\:y}(x^{3}-y^{3}+2xy)
laplacetransform cos(t)*cos(pi)	laplacetransform\:\cos(t)\cdot\:\cos(π)
integral of sin^5(3x)cos(3x)	\int\:\sin^{5}(3x)\cos(3x)dx
tangent of f(x)=x^2-5,(-4,11)	tangent\:f(x)=x^{2}-5,(-4,11)
integral from 0 to 10 of 1000te^{-0.5t}	\int\:_{0}^{10}1000te^{-0.5t}dt
d/(dθ)(e^{iθ})	\frac{d}{dθ}(e^{iθ})
integral of 2cos^2(θ)-1/2	\int\:2\cos^{2}(θ)-\frac{1}{2}dθ
(\partial)/(\partial y)((x^2-2x)cos(y))	\frac{\partial\:}{\partial\:y}((x^{2}-2x)\cos(y))
(\partial ^2)/(\partial x^2)(ln(2+x^2y^2))	\frac{\partial\:^{2}}{\partial\:x^{2}}(\ln(2+x^{2}y^{2}))
integral of tan^3(2x)	\int\:\tan^{3}(2x)dx
tangent of y=f(x),\at x=7	tangent\:y=f(x),\at\:x=7
derivative of 5^{7-x^2}	derivative\:5^{7-x^{2}}
laplacetransform 8t	laplacetransform\:8t
area x^2-6x,-x^2+4x	area\:x^{2}-6x,-x^{2}+4x
derivative of f(t)=sqrt(3t^2-t)	derivative\:f(t)=\sqrt{3t^{2}-t}
integral of (2x^2+x+1)/(x^3+2x^2+x)	\int\:\frac{2x^{2}+x+1}{x^{3}+2x^{2}+x}dx
derivative of sqrt(x^2+2x)	\frac{d}{dx}(\sqrt{x^{2}+2x})
derivative of y=((x^2+1)/(x^2-1))^6	derivative\:y=(\frac{x^{2}+1}{x^{2}-1})^{6}
derivative of cos(3xcos(2x))	\frac{d}{dx}(\cos(3x)\cos(2x))
tangent of f(x)=sqrt(7-6x),\at x=-1	tangent\:f(x)=\sqrt{7-6x},\at\:x=-1
derivative of ln(tan(x/2+pi/4))	\frac{d}{dx}(\ln(\tan(\frac{x}{2}+\frac{π}{4})))
integral of 9e^{3t}	\int\:9e^{3t}dt
derivative of log_{5}(2x-5)	\frac{d}{dx}(\log_{5}(2x-5))

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