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Popular Calculus Problems

integral of cos(t)tan(t)	\int\:\cos(t)\tan(t)dt
derivative of x^4e^{4x}	\frac{d}{dx}(x^{4}e^{4x})
y^'=y(xy^4-1)	y^{\prime\:}=y(xy^{4}-1)
x^2(dy)/(dx)+xy=x^3+1	x^{2}\frac{dy}{dx}+xy=x^{3}+1
derivative of 2x+6	\frac{d}{dx}(2x+6)
limit as x approaches infinity of x/(sqrt(x^3+6))	\lim\:_{x\to\:\infty\:}(\frac{x}{\sqrt{x^{3}+6}})
(\partial)/(\partial x)(ln(x+z))	\frac{\partial\:}{\partial\:x}(\ln(x+z))
integral of 5sin(6x)+6sin(5x)	\int\:5\sin(6x)+6\sin(5x)dx
derivative of (x-2^3(x-1))	\frac{d}{dx}((x-2)^{3}(x-1))
derivative of (x-1)/(x+1)	derivative\:\frac{x-1}{x+1}
derivative of y=(2x+1)^3+6x(2x+1)^2	derivative\:y=(2x+1)^{3}+6x(2x+1)^{2}
(\partial)/(\partial y)(e^{-3x}cos(6y))	\frac{\partial\:}{\partial\:y}(e^{-3x}\cos(6y))
(dy)/(dx)=ytan(x)	\frac{dy}{dx}=y\tan(x)
integral of x+12x^2	\int\:x+12x^{2}dx
f(x)=(x-2)^2(x-3)^3	f(x)=(x-2)^{2}(x-3)^{3}
integral of (x+2)/(x^2+x)	\int\:\frac{x+2}{x^{2}+x}dx
implicit (dy)/(dx),sqrt(xy)=x^7y+72	implicit\:\frac{dy}{dx},\sqrt{xy}=x^{7}y+72
limit as x approaches-infinity of ln(x-2)	\lim\:_{x\to\:-\infty\:}(\ln(x-2))
derivative of y=(tan(1/x))^{sec(1/x)}	derivative\:y=(\tan(\frac{1}{x}))^{\sec(\frac{1}{x})}
limit as x approaches 1 of (x^2-sqrt(x))/(1-x)	\lim\:_{x\to\:1}(\frac{x^{2}-\sqrt{x}}{1-x})
integral of \sqrt[3]{ax^2}	\int\:\sqrt[3]{ax^{2}}dx
integral of (3^{2x})/(1+3^{2x)}	\int\:\frac{3^{2x}}{1+3^{2x}}dx
limit as x approaches infinity of tan(7/x)	\lim\:_{x\to\:\infty\:}(\tan(\frac{7}{x}))
derivative of 6x^2+15xy+3y^2	\frac{d}{dx}(6x^{2}+15xy+3y^{2})
integral of (e^xx)	\int\:(e^{x}x)dx
limit as x approaches infinity of ((e^{2x}-8-19x))/((19x)^2)	\lim\:_{x\to\:\infty\:}(\frac{(e^{2x}-8-19x)}{(19x)^{2}})
y^{''}+49y=0	y^{\prime\:\prime\:}+49y=0
integral of 64sin^2(x)	\int\:64\sin^{2}(x)dx
tangent of f(x)=x^3-11x,\at x=3	tangent\:f(x)=x^{3}-11x,\at\:x=3
sum from n=2 to infinity of (3/4)^n	\sum\:_{n=2}^{\infty\:}(\frac{3}{4})^{n}
derivative of (4x^5-2x(3x+e^x))	\frac{d}{dx}((4x^{5}-2x)(3x+e^{x}))
derivative of 7/(sqrt(t))	derivative\:\frac{7}{\sqrt{t}}
limit as x approaches infinity of 2x^3-5x-4x^3	\lim\:_{x\to\:\infty\:}(2x^{3}-5x-4x^{3})
derivative of (x-2)^{1/3}	derivative\:(x-2)^{\frac{1}{3}}
integral of cot^3(6x)	\int\:\cot^{3}(6x)dx
integral from 0 to 1 of 2/(2x^2+3x+1)	\int\:_{0}^{1}\frac{2}{2x^{2}+3x+1}dx
integral of 9+1/x	\int\:9+\frac{1}{x}dx
d/(dt)(1+3t)	\frac{d}{dt}(1+3t)
integral of sec(θ)tan(θ)	\int\:\sec(θ)\tan(θ)dθ
integral of-56cos(7z-5)	\int\:-56\cos(7z-5)dz
integral of (6x^2+2x+7)/(x^3-1)	\int\:\frac{6x^{2}+2x+7}{x^{3}-1}dx
d/(dθ)((1+2sin(θ))sin(θ))	\frac{d}{dθ}((1+2\sin(θ))\sin(θ))
integral of t^2sqrt(1+t^3)	\int\:t^{2}\sqrt{1+t^{3}}dt
integral of 1/(sec(sqrt(y)))	\int\:\frac{1}{\sec(\sqrt{y})}dy
integral of ((x^2+4))/(x+2)	\int\:\frac{(x^{2}+4)}{x+2}dx
integral of 1/(sin(x)+3cos(x)+1)	\int\:\frac{1}{\sin(x)+3\cos(x)+1}dx
derivative of sqrt(sin(e^{x^3sin(x))})	\frac{d}{dx}(\sqrt{\sin(e^{x^{3}\sin(x)})})
derivative of x^2-8x+12	\frac{d}{dx}(x^{2}-8x+12)
integral of 1/(8-3x)	\int\:\frac{1}{8-3x}dx
integral from 0 to 1 of-ln(x)	\int\:_{0}^{1}-\ln(x)dx
(dy)/(dx)=-y(x+1)	\frac{dy}{dx}=-y(x+1)
derivative of x+4sqrt(x+2)	derivative\:x+4\sqrt{x+2}
limit as x approaches 3 of (1/3 sqrt(x)-sqrt(1/3))/(x-3)	\lim\:_{x\to\:3}(\frac{\frac{1}{3}\sqrt{x}-\sqrt{\frac{1}{3}}}{x-3})
derivative of 8cos(x)	derivative\:8\cos(x)
derivative of sqrt(2t+1)	derivative\:\sqrt{2t+1}
limit as x approaches infinity of x^2-25	\lim\:_{x\to\:\infty\:}(x^{2}-25)
(dy)/(dx)+8y=6	\frac{dy}{dx}+8y=6
laplacetransform 2-t	laplacetransform\:2-t
derivative of (2x+5)^3(x^5+3)^6	derivative\:(2x+5)^{3}(x^{5}+3)^{6}
integral of (16x)/(sqrt(1-x^4))	\int\:\frac{16x}{\sqrt{1-x^{4}}}dx
derivative of sqrt(x^3+5)	\frac{d}{dx}(\sqrt{x^{3}+5})
(dy)/(dx)=8xe^{7y}	\frac{dy}{dx}=8xe^{7y}
integral of (-7)/(sqrt(x^2+16))	\int\:\frac{-7}{\sqrt{x^{2}+16}}dx
limit as x approaches 5 of ((ln(x/5)))/(x^2-25)	\lim\:_{x\to\:5}(\frac{(\ln(\frac{x}{5}))}{x^{2}-25})
integral of 1/(ln(x^x))	\int\:\frac{1}{\ln(x^{x})}dx
integral of x/(12)	\int\:\frac{x}{12}dx
limit as x approaches-2 of (x^2)/(x-1)	\lim\:_{x\to\:-2}(\frac{x^{2}}{x-1})
derivative of (sin(x^2))/(x^2)	derivative\:\frac{\sin(x^{2})}{x^{2}}
integral of (1+sqrt(x)+x)/(sqrt(x))	\int\:\frac{1+\sqrt{x}+x}{\sqrt{x}}dx
(dy}{dx}=\frac{13x)/y	\frac{dy}{dx}=\frac{13x}{y}
derivative of x\|x\|	derivative\:x\left\|x\right\|
integral of (3x)/1	\int\:\frac{3x}{1}dx
sum from n=1 to infinity of 2n+1	\sum\:_{n=1}^{\infty\:}2n+1
limit as x approaches 1/2 of xtan(pi)x	\lim\:_{x\to\:\frac{1}{2}}(x\tan(π)x)
limit as x approaches 3/2 of (8x^3-27)/(2x-3)	\lim\:_{x\to\:\frac{3}{2}}(\frac{8x^{3}-27}{2x-3})
derivative of x^2e^x+2xe^x	\frac{d}{dx}(x^{2}e^{x}+2xe^{x})
limit as x approaches infinity of (ln(5))/((1+ln(x)))	\lim\:_{x\to\:\infty\:}(\frac{\ln(5)}{(1+\ln(x))})
limit as x approaches 0+of sqrt(x)e^{sin(pi/x)}	\lim\:_{x\to\:0+}(\sqrt{x}e^{\sin(\frac{π}{x})})
derivative of ((10+x/pi)^{1/3})	\frac{d}{dx}((\frac{10+x}{π})^{\frac{1}{3}})
integral of-1/(1-x)	\int\:-\frac{1}{1-x}dx
(\partial)/(\partial x)(z*arctan(y/x))	\frac{\partial\:}{\partial\:x}(z\cdot\:\arctan(\frac{y}{x}))
integral from 2 to infinity of (8cos(pi/x))/(x^2)	\int\:_{2}^{\infty\:}\frac{8\cos(\frac{π}{x})}{x^{2}}dx
limit as h approaches+0 of (1/(a+h)-1/a)/h	\lim\:_{h\to\:+0}(\frac{\frac{1}{a+h}-\frac{1}{a}}{h})
d/(dt)(sqrt(t))	\frac{d}{dt}(\sqrt{t})
integral of t^{-3}	\int\:t^{-3}dt
integral of (x^3)/(sqrt(25+x^2))	\int\:\frac{x^{3}}{\sqrt{25+x^{2}}}dx
tangent of f(x)=-3x^2+12,\at x=3	tangent\:f(x)=-3x^{2}+12,\at\:x=3
8x^2y+y^'=10x^2	8x^{2}y+y^{\prime\:}=10x^{2}
derivative of 4x^3-33x^2+84x-60	derivative\:4x^{3}-33x^{2}+84x-60
derivative of 2xsqrt(16-x^2)	\frac{d}{dx}(2x\sqrt{16-x^{2}})
(\partial)/(\partial x)(2x^2+y^3)	\frac{\partial\:}{\partial\:x}(2x^{2}+y^{3})
derivative of f(x)=(2x^{3/2}-x^2+4)/x	derivative\:f(x)=\frac{2x^{\frac{3}{2}}-x^{2}+4}{x}
derivative of (500)/(12+5e^{-0.5t)}	derivative\:\frac{500}{12+5e^{-0.5t}}
implicit (dy)/(dx),x=y^3-8y^2+5,(-2,1)	implicit\:\frac{dy}{dx},x=y^{3}-8y^{2}+5,(-2,1)
inverse oflaplace 1/(s^2-2s-3)	inverselaplace\:\frac{1}{s^{2}-2s-3}
limit as x approaches 0+of (x-[x])/([x]-2x)	\lim\:_{x\to\:0+}(\frac{x-[x]}{[x]-2x})
derivative of x^2log_{2}(7-6x)	\frac{d}{dx}(x^{2}\log_{2}(7-6x))
integral of 6sin^2(3x)cos(3x)ln(sin(3x))	\int\:6\sin^{2}(3x)\cos(3x)\ln(\sin(3x))dx
integral from 0 to 4 of 4sqrt(x)-2x	\int\:_{0}^{4}4\sqrt{x}-2xdx
(dy)/(dx)=e^{3x}+9y	\frac{dy}{dx}=e^{3x}+9y

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