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Popular Calculus Problems

integral of (3x^2+2x+1)/x	\int\:\frac{3x^{2}+2x+1}{x}dx
derivative of (sin(2x)/x)	\frac{d}{dx}(\frac{\sin(2x)}{x})
integral of sin^2(4θ)	\int\:\sin^{2}(4θ)dθ
laplacetransform f(t)=5cos(8t)+3e^{-4}sin(3t)	laplacetransform\:f(t)=5\cos(8t)+3e^{-4}\sin(3t)
derivative of (x^3+1^4)	\frac{d}{dx}((x^{3}+1)^{4})
integral of sec(x)-cos(x)	\int\:\sec(x)-\cos(x)dx
derivative of 1/2 ln(x)	derivative\:\frac{1}{2}\ln(x)
integral of xln(sqrt(11)x)	\int\:x\ln(\sqrt{11}x)dx
limit as x approaches (3pi)/2 of sin(x)	\lim\:_{x\to\:\frac{3π}{2}}(\sin(x))
derivative of f(y)=ln(5x^2-x+1)	derivative\:f(y)=\ln(5x^{2}-x+1)
integral of v/(3-0.001v^2)	\int\:\frac{v}{3-0.001v^{2}}dv
(\partial)/(\partial x)(y+arctan(y/x))	\frac{\partial\:}{\partial\:x}(y+\arctan(\frac{y}{x}))
(\partial)/(\partial y)(x^3-y^2)	\frac{\partial\:}{\partial\:y}(x^{3}-y^{2})
taylor ln(6x+1)	taylor\:\ln(6x+1)
limit as x approaches infinity of (e^{5x-3})/(ln(x-2))	\lim\:_{x\to\:\infty\:}(\frac{e^{5x-3}}{\ln(x-2)})
derivative of f(x)=cos(a^8+x^8)	derivative\:f(x)=\cos(a^{8}+x^{8})
integral from 0 to infinity of x^1e^{-x}	\int\:_{0}^{\infty\:}x^{1}e^{-x}dx
derivative of ln((5x^2+9^3))	\frac{d}{dx}(\ln((5x^{2}+9)^{3}))
integral of (sqrt(sin(2x))-cos(2x))^2	\int\:(\sqrt{\sin(2x)}-\cos(2x))^{2}dx
(\partial)/(\partial x)(e^{6xe^y})	\frac{\partial\:}{\partial\:x}(e^{6xe^{y}})
derivative of (sqrt(3x)/4)	\frac{d}{dx}(\frac{\sqrt{3x}}{4})
derivative of 7/(3x^2)	derivative\:\frac{7}{3x^{2}}
(\partial)/(\partial x)(sin^3(2x))	\frac{\partial\:}{\partial\:x}(\sin^{3}(2x))
integral from 0 to pi of 3xsin(x)	\int\:_{0}^{π}3x\sin(x)dx
inverse oflaplace s/(s^4+4)	inverselaplace\:\frac{s}{s^{4}+4}
derivative of 20cos(x)	\frac{d}{dx}(20\cos(x))
(\partial)/(\partial x)(5x^2+y^2)	\frac{\partial\:}{\partial\:x}(5x^{2}+y^{2})
integral of 4xln(7x)	\int\:4x\ln(7x)dx
(dv)/(dt)=9.8-0.6	\frac{dv}{dt}=9.8-0.6
integral from 1 to 4 of 2pix(-3/2 x+6)	\int\:_{1}^{4}2πx(-\frac{3}{2}x+6)dx
derivative of f(x)=x^3(2x-1)	derivative\:f(x)=x^{3}(2x-1)
limit as x approaches 0+of (sin(x))/(x^{1/2)}	\lim\:_{x\to\:0+}(\frac{\sin(x)}{x^{\frac{1}{2}}})
integral from-infinity to 0 of x^2e^{-x}	\int\:_{-\infty\:}^{0}x^{2}e^{-x}dx
derivative of (1-xe^x)	\frac{d}{dx}((1-x)e^{x})
area 2y=3sqrt(x),2y+3x=6,y=4	area\:2y=3\sqrt{x},2y+3x=6,y=4
integral from pi/2 to pi of cos(x)	\int\:_{\frac{π}{2}}^{π}\cos(x)dx
integral of 1/(e^x+4e^{-x)}	\int\:\frac{1}{e^{x}+4e^{-x}}dx
integral from 1 to 3 of 2pix(-x^2+4x-3)	\int\:_{1}^{3}2πx(-x^{2}+4x-3)dx
derivative of y=x^{3/2}(x+ce^x)	derivative\:y=x^{\frac{3}{2}}(x+ce^{x})
integral of 10-(14-2(16-2x)^{1/2})	\int\:10-(14-2(16-2x)^{\frac{1}{2}})dx
integral of x^4-8x^2+16	\int\:x^{4}-8x^{2}+16dx
limit as x approaches-3 of x/((x+3)^4)	\lim\:_{x\to\:-3}(\frac{x}{(x+3)^{4}})
y^{''}-ky=kxe^{-x}	y^{\prime\:\prime\:}-ky=kxe^{-x}
derivative of 4sqrt(2)	\frac{d}{dx}(4\sqrt{2})
y^{''}+9y=e^t,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+9y=e^{t},y(0)=0,y^{\prime\:}(0)=0
integral of e^{(3x+1)}	\int\:e^{(3x+1)}dx
limit as x approaches 27 of (x-27)/(sqrt(x+9-6))	\lim\:_{x\to\:27}(\frac{x-27}{\sqrt{x+9-6}})
area 4x,x^2	area\:4x,x^{2}
integral from 3 to 9 of 1/(xln(x))	\int\:_{3}^{9}\frac{1}{x\ln(x)}dx
tangent of y=sqrt(2x+1),\at x= 1/2	tangent\:y=\sqrt{2x+1},\at\:x=\frac{1}{2}
(\partial)/(\partial x)(2/((x-3t)^2+1))	\frac{\partial\:}{\partial\:x}(\frac{2}{(x-3t)^{2}+1})
integral of (x-4)	\int\:(x-4)dx
d/(dθ)(5/(2cos(θ)+7sin(θ)))	\frac{d}{dθ}(\frac{5}{2\cos(θ)+7\sin(θ)})
tangent of f(x)=3x^4-8x^3+2	tangent\:f(x)=3x^{4}-8x^{3}+2
derivative of 5e^{-2x}sin(3x)	\frac{d}{dx}(5e^{-2x}\sin(3x))
maclaurin (1+x)^{-5/3}	maclaurin\:(1+x)^{-\frac{5}{3}}
(\partial)/(\partial x)(ln(xy))	\frac{\partial\:}{\partial\:x}(\ln(xy))
limit as x approaches 9 of x+7	\lim\:_{x\to\:9}(x+7)
d/(dt)(10^{2sqrt(t)})	\frac{d}{dt}(10^{2\sqrt{t}})
derivative of y=x^{2/5}(x+3)	derivative\:y=x^{\frac{2}{5}}(x+3)
derivative of (x^3-4/(x-1))	\frac{d}{dx}(\frac{x^{3}-4}{x-1})
integral of (3x-2)/(x+1)	\int\:\frac{3x-2}{x+1}dx
limit as x approaches-3 of \|-x-1\|	\lim\:_{x\to\:-3}(\left\|-x-1\right\|)
integral of 1/((x-3)(x-1))	\int\:\frac{1}{(x-3)(x-1)}dx
derivative of 6/5-6/5 e^{-20t}	derivative\:\frac{6}{5}-\frac{6}{5}e^{-20t}
longdivision (x^2+1)/(x^2-4)	longdivision\:\frac{x^{2}+1}{x^{2}-4}
(dy)/(dx)=4-y	\frac{dy}{dx}=4-y
integral of (x^3)/9	\int\:\frac{x^{3}}{9}dx
derivative of f(x)=(7x)/(3+x^2)	derivative\:f(x)=\frac{7x}{3+x^{2}}
taylor sqrt(x),x=4	taylor\:\sqrt{x},x=4
integral from 0 to pi/8 of cos^2(2x)	\int\:_{0}^{\frac{π}{8}}\cos^{2}(2x)dx
taylor x^5cos(x^2)	taylor\:x^{5}\cos(x^{2})
integral of sqrt(ax+b)	\int\:\sqrt{ax+b}dx
derivative of in(xinx)	\frac{d}{dx}(in(xinx))
derivative of 11-x+4ln(2x-1)	\frac{d}{dx}(11-x+4\ln(2x-1))
integral of ((e^x-1)/(e^x+1))	\int\:(\frac{e^{x}-1}{e^{x}+1})dx
integral of e^{e^t}	\int\:e^{e^{t}}dt
integral of x/(\sqrt[3]{x+8)}	\int\:\frac{x}{\sqrt[3]{x+8}}dx
laplacetransform e^{3t}cos(6t)	laplacetransform\:e^{3t}\cos(6t)
integral of 3a^7x^6	\int\:3a^{7}x^{6}dx
integral of (x+1)e^{-x}	\int\:(x+1)e^{-x}dx
integral of xe^{0.2x}	\int\:xe^{0.2x}dx
derivative of f(x)=x^3+3x	derivative\:f(x)=x^{3}+3x
derivative of f(x)=(x+9)/(x-9)	derivative\:f(x)=\frac{x+9}{x-9}
derivative of xcos(3x)	derivative\:x\cos(3x)
derivative of 2sin(x-3cos(x))	\frac{d}{dx}(2\sin(x)-3\cos(x))
derivative of y=sqrt(4+3x)	derivative\:y=\sqrt{4+3x}
limit as x approaches 25 of 2x+2sqrt(x)	\lim\:_{x\to\:25}(2x+2\sqrt{x})
limit as x approaches 3 of (x-1)/(x^2-2)	\lim\:_{x\to\:3}(\frac{x-1}{x^{2}-2})
xy^2dx=dy-xdx	xy^{2}dx=dy-xdx
limit as x approaches 0 of sin((4pi)/x)	\lim\:_{x\to\:0}(\sin(\frac{4π}{x}))
limit as x approaches 0 of (tan(9x))/x	\lim\:_{x\to\:0}(\frac{\tan(9x)}{x})
integral of sqrt(144-4x^2)	\int\:\sqrt{144-4x^{2}}dx
derivative of 12arccot(ax^2)	\frac{d}{dx}(12\arccot(ax^{2}))
integral from 0 to pi/4 of tan^5(x)	\int\:_{0}^{\frac{π}{4}}\tan^{5}(x)dx
integral from 0 to pi of 19sin^2(4x)	\int\:_{0}^{π}19\sin^{2}(4x)dx
(3x^2y^2+y)dx+(2x^3y+x)dy=0	(3x^{2}y^{2}+y)dx+(2x^{3}y+x)dy=0
integral from 0 to pi/6 of cos^3(x)	\int\:_{0}^{\frac{π}{6}}\cos^{3}(x)dx
integral of 16xln(7x)	\int\:16x\ln(7x)dx
integral from 0 to pi/2 of 11sin^2(2x)	\int\:_{0}^{\frac{π}{2}}11\sin^{2}(2x)dx

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