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Popular Calculus Problems

(\partial)/(\partial x)(ln(x^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}))
inverse oflaplace (15)/(s^2+2s+5)	inverselaplace\:\frac{15}{s^{2}+2s+5}
integral of 1/(cos^2(θ)sqrt(1+tan(θ)))	\int\:\frac{1}{\cos^{2}(θ)\sqrt{1+\tan(θ)}}dθ
(dx)/(dt)=a-bx	\frac{dx}{dt}=a-bx
derivative of y=(5-3x^2)^3	derivative\:y=(5-3x^{2})^{3}
tangent of x^4-2x^2+1	tangent\:x^{4}-2x^{2}+1
derivative of 2e^{4x}sin(pix)	\frac{d}{dx}(2e^{4x}\sin(π)x)
derivative of e^{4^x}	\frac{d}{dx}(e^{4^{x}})
sum from n=1 to infinity of 1/((n^2+5n))	\sum\:_{n=1}^{\infty\:}\frac{1}{(n^{2}+5n)}
integral of (sin(ln(x))cos(2ln(x)))/(2x)	\int\:\frac{\sin(\ln(x))\cos(2\ln(x))}{2x}dx
derivative of x/(3-x^2)	\frac{d}{dx}(\frac{x}{3-x^{2}})
4ydx-xy-3xdy=0	4ydx-xy-3xdy=0
derivative of (x+2(2x^2-3))	\frac{d}{dx}((x+2)(2x^{2}-3))
derivative of 9x^8	\frac{d}{dx}(9x^{8})
tangent of x^2-9	tangent\:x^{2}-9
f(x)=\sqrt[5]{ln(x)}	f(x)=\sqrt[5]{\ln(x)}
(\partial)/(\partial x)((3y^2)/((5x+3y)^2))	\frac{\partial\:}{\partial\:x}(\frac{3y^{2}}{(5x+3y)^{2}})
y^{''}-6y^'+9y=0,y(0)=-2,y^'(0)=1	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=-2,y^{\prime\:}(0)=1
integral of 1/x-x^2+sin(x)-3^x	\int\:\frac{1}{x}-x^{2}+\sin(x)-3^{x}dx
(dy)/(dx)+2y=9e^x	\frac{dy}{dx}+2y=9e^{x}
(\partial)/(\partial y)(3x+8y+2)	\frac{\partial\:}{\partial\:y}(3x+8y+2)
(\partial)/(\partial x)(yln(y))	\frac{\partial\:}{\partial\:x}(y\ln(y))
integral of sin(8x)cos(6x)	\int\:\sin(8x)\cos(6x)dx
2xy^'-y=x^2	2xy^{\prime\:}-y=x^{2}
integral from 6 to 8 of x/(x^2+4x+13)	\int\:_{6}^{8}\frac{x}{x^{2}+4x+13}dx
derivative of xln(x+(3x^2-2)^3)	\frac{d}{dx}(x\cdot\:\ln(x)+(3\cdot\:x^{2}-2)^{3})
y^{''}-2y^'+y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}+y=0,y(0)=1,y^{\prime\:}(0)=0
integral of 14x^{3/2}	\int\:14x^{\frac{3}{2}}dx
integral of (y^2)/3	\int\:\frac{y^{2}}{3}dy
(2ln(x))^'	(2\ln(x))^{\prime\:}
derivative of x^3e^{x^3}	\frac{d}{dx}(x^{3}e^{x^{3}})
integral of (x+5)^7	\int\:(x+5)^{7}dx
limit as x approaches 0 of (sin(ax))/x	\lim\:_{x\to\:0}(\frac{\sin(ax)}{x})
limit as x approaches pi/2 of-cot(x)+1	\lim\:_{x\to\:\frac{π}{2}}(-\cot(x)+1)
integral of (x^2+12x+12)/(x(x+2)(x-2))	\int\:\frac{x^{2}+12x+12}{x(x+2)(x-2)}dx
integral of 1/(3x^2)	\int\:\frac{1}{3x^{2}}dx
integral of (e^x)/(sqrt(1-e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1-e^{2x}}}dx
integral of sqrt(x-1)	\int\:\sqrt{x-1}dx
integral from 1 to 2 of xsqrt(x-1)	\int\:_{1}^{2}x\sqrt{x-1}dx
inverse oflaplace 1/(s^2(s+1/15))	inverselaplace\:\frac{1}{s^{2}(s+\frac{1}{15})}
derivative of ax^4	\frac{d}{dx}(ax^{4})
sum from n=1 to infinity of n^2(5/6)^n	\sum\:_{n=1}^{\infty\:}n^{2}(\frac{5}{6})^{n}
integral of (1-3y)^2-(1-y^2)^2	\int\:(1-3y)^{2}-(1-y^{2})^{2}dy
(\partial)/(\partial x)(((5x+4))/(5y+1))	\frac{\partial\:}{\partial\:x}(\frac{(5x+4)}{5y+1})
integral of 2θsec^2(θ)	\int\:2θ\sec^{2}(θ)dθ
derivative of 3x-pi	\frac{d}{dx}(3x-π)
derivative of (x^4/(16))	\frac{d}{dx}(\frac{x^{4}}{16})
(d^2)/(dx^2)(3x^2)	\frac{d^{2}}{dx^{2}}(3x^{2})
limit as x approaches 0 of 2/3 x^{-1/3}	\lim\:_{x\to\:0}(\frac{2}{3}x^{-\frac{1}{3}})
integral of e^t-1	\int\:e^{t}-1dt
integral from-6 to 6 of (e^x-e^{-x})^2	\int\:_{-6}^{6}(e^{x}-e^{-x})^{2}dx
derivative of (cos(t))/(t^7)	derivative\:\frac{\cos(t)}{t^{7}}
(\partial)/(\partial b)((ab)/(2c+15))	\frac{\partial\:}{\partial\:b}(\frac{ab}{2c+15})
limit as x approaches 0 of xe^{2x}	\lim\:_{x\to\:0}(xe^{2x})
limit as x approaches 0 of 4/(xcsc(x))	\lim\:_{x\to\:0}(\frac{4}{x\csc(x)})
area y=3(x^3-x),y=0	area\:y=3(x^{3}-x),y=0
integral from-1 to 2 of (2x-1)(4x+5)	\int\:_{-1}^{2}(2x-1)(4x+5)dx
y^'=-x/y+((x^2+y^2))/y	y^{\prime\:}=-\frac{x}{y}+\frac{(x^{2}+y^{2})}{y}
integral from c to i of nt_{a}^b1+x+y	\int\:_{c}^{d}\int\:_{a}^{b}1+x+ydxdy
integral of 1/(2x^2+4)	\int\:\frac{1}{2x^{2}+4}dx
integral of 1/(a^2sin^2(x)+b^2cos^2(x))	\int\:\frac{1}{a^{2}\sin^{2}(x)+b^{2}\cos^{2}(x)}dx
(\partial)/(\partial x)(xe^{-x}(y^2-4y))	\frac{\partial\:}{\partial\:x}(xe^{-x}(y^{2}-4y))
integral of (3x)/(\sqrt[3]{x^2+3)}	\int\:\frac{3x}{\sqrt[3]{x^{2}+3}}dx
(\partial)/(\partial x)(1/(sqrt(x^2+a^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{x^{2}+a^{2}}})
derivative of (x^2)/(3(1-x))	derivative\:\frac{x^{2}}{3(1-x)}
inverse oflaplace 7/(s^2+5s+10)	inverselaplace\:\frac{7}{s^{2}+5s+10}
(20+x^2)y^'-2xy=0	(20+x^{2})y^{\prime\:}-2xy=0
derivative of sqrt((x^2+1))	\frac{d}{dx}(\sqrt{(x^{2}+1)})
derivative of (4x-3)^4	derivative\:(4x-3)^{4}
derivative of f(x)=(-9x^2+4)^2	derivative\:f(x)=(-9x^{2}+4)^{2}
integral of xarctan(7x)	\int\:x\arctan(7x)dx
(dy)/(dt)=5-2y	\frac{dy}{dt}=5-2y
integral of sin(wx)	\int\:\sin(wx)dx
derivative of f(x)=9x^3	derivative\:f(x)=9x^{3}
limit as z approaches 0 of (sin(z))/z	\lim\:_{z\to\:0}(\frac{\sin(z)}{z})
integral of sqrt(2+\sqrt{x)}	\int\:\sqrt{2+\sqrt{x}}dx
limit as x approaches 1 of ax^2+bx+c	\lim\:_{x\to\:1}(ax^{2}+bx+c)
limit as x approaches+0+of 1/(x^{2/3)}	\lim\:_{x\to\:+0+}(\frac{1}{x^{\frac{2}{3}}})
derivative of x^2+3	derivative\:x^{2}+3
integral from 0 to 6 of 2pi(6-x)(6x-x^2)	\int\:_{0}^{6}2π(6-x)(6x-x^{2})dx
integral of 3e^x+2sin(x)	\int\:3e^{x}+2\sin(x)dx
derivative of (x-0.5/((x+0.5+i)^2))	\frac{d}{dx}(\frac{x-0.5}{(x+0.5+i)^{2}})
limit as x approaches infinity of x/(\sqrt[3]{x^3+10)}	\lim\:_{x\to\:\infty\:}(\frac{x}{\sqrt[3]{x^{3}+10}})
tangent of y=x^4+3e^x,(0,3)	tangent\:y=x^{4}+3e^{x},(0,3)
integral of x(sin(x)-2)	\int\:x(\sin(x)-2)dx
(\partial)/(\partial x)(4^{(x^9)})	\frac{\partial\:}{\partial\:x}(4^{(x^{9})})
(d^2)/(dx^2)(4cos(x))	\frac{d^{2}}{dx^{2}}(4\cos(x))
derivative of f(x)= 4/(x^5)	derivative\:f(x)=\frac{4}{x^{5}}
limit as x approaches-2 of x^2+5x	\lim\:_{x\to\:-2}(x^{2}+5x)
limit as x approaches 2 of 3x+3	\lim\:_{x\to\:2}(3x+3)
derivative of ln((x-3)/(x+3))	derivative\:\ln(\frac{x-3}{x+3})
derivative of x+sin(2x)	\frac{d}{dx}(x+\sin(2x))
derivative of ((x^2+2^{3/2})/3)	\frac{d}{dx}(\frac{(x^{2}+2)^{\frac{3}{2}}}{3})
integral from 0 to 27 of 3/(x^{2/3)}	\int\:_{0}^{27}\frac{3}{x^{\frac{2}{3}}}dx
derivative of 11e^{x^2}	derivative\:11e^{x^{2}}
integral of-1(x-4)	\int\:-1(x-4)dx
limit as t approaches pi of t/pi	\lim\:_{t\to\:π}(\frac{t}{π})
derivative of (2x^2+7(8x-4))	\frac{d}{dx}((2x^{2}+7)(8x-4))
area y=sqrt(3-x),y=x-1,y=-sqrt(3-x)	area\:y=\sqrt{3-x},y=x-1,y=-\sqrt{3-x}
derivative of x^{-1/2}*cos(x)	\frac{d}{dx}(x^{-\frac{1}{2}}\cdot\:\cos(x))

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