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Popular Calculus Problems

integral of (4-4x)^7	\int\:(4-4x)^{7}dx
sum from n=1 to infinity of-(2/3)^{n-1}	\sum\:_{n=1}^{\infty\:}-(\frac{2}{3})^{n-1}
d/(dθ)(cot^2(sin(θ)))	\frac{d}{dθ}(\cot^{2}(\sin(θ)))
5(ln(y))y^'-x^3y=0	5(\ln(y))y^{\prime\:}-x^{3}y=0
integral of 8sqrt(tan(x))sec^4(x)	\int\:8\sqrt{\tan(x)}\sec^{4}(x)dx
(tan(x/2))^'	(\tan(\frac{x}{2}))^{\prime\:}
limit as t approaches 0 of t(ln(t))	\lim\:_{t\to\:0}(t(\ln(t)))
integral from-1 to 0 of xsqrt(1-x^2)	\int\:_{-1}^{0}x\sqrt{1-x^{2}}dx
derivative of a(sin(x-xcos(x)))	\frac{d}{dx}(a(\sin(x)-x\cos(x)))
integral of xln(x-2)	\int\:x\ln(x-2)dx
integral of (e^x)/(1-e^x)	\int\:\frac{e^{x}}{1-e^{x}}dx
derivative of xsqrt(3)-2x^2	\frac{d}{dx}(x\sqrt{3}-2x^{2})
integral from 0 to 1 of 4(1+sqrt(x))^7	\int\:_{0}^{1}4(1+\sqrt{x})^{7}dx
derivative of 800sqrt(x^2-0.1x)	\frac{d}{dx}(800\sqrt{x^{2}-0.1x})
integral of cot(x)sec(x)	\int\:\cot(x)\sec(x)dx
integral of (x+6)/((x+1)^2)	\int\:\frac{x+6}{(x+1)^{2}}dx
(\partial ^2)/(\partial r\partial θ)(r(θ)cos(θ))	\frac{\partial\:^{2}}{\partial\:r\partial\:θ}(r(θ)\cos(θ))
limit as x approaches 0 of (x^2+1)/(x-1)	\lim\:_{x\to\:0}(\frac{x^{2}+1}{x-1})
(x+y+1)dx-(y-x+3)dy=0	(x+y+1)dx-(y-x+3)dy=0
limit as x approaches-1 of 7\|x+1\|-4	\lim\:_{x\to\:-1}(7\left\|x+1\right\|-4)
integral of sqrt(e^{2x)}	\int\:\sqrt{e^{2x}}dx
integral of (x(6x^2+6))/(x^2+1)	\int\:\frac{x(6x^{2}+6)}{x^{2}+1}dx
derivative of-2sin(x-sin(2x))	\frac{d}{dx}(-2\sin(x)-\sin(2x))
derivative of (x+1e^{arctan(x)})	\frac{d}{dx}((x+1)e^{\arctan(x)})
(\partial)/(\partial y)(xy^2+5)	\frac{\partial\:}{\partial\:y}(xy^{2}+5)
integral of x/((x^2+1)^{5/2)}	\int\:\frac{x}{(x^{2}+1)^{\frac{5}{2}}}dx
integral of (y^3)/(y^4+1)	\int\:\frac{y^{3}}{y^{4}+1}dy
(x^2+1)y^'+3x(y-1)=0,y(0)=8	(x^{2}+1)y^{\prime\:}+3x(y-1)=0,y(0)=8
integral of (sin(cx))/(cos^2(cx))	\int\:\frac{\sin(cx)}{\cos^{2}(cx)}dx
derivative of (14x+8x^2)/((7+8x)^2)	derivative\:\frac{14x+8x^{2}}{(7+8x)^{2}}
d/(dt)x+7x=5cos(2t)	\frac{d}{dt}x+7x=5\cos(2t)
integral from 1 to sqrt(3 of)x3^{x^2}	\int\:_{1}^{\sqrt{3}}x3^{x^{2}}dx
derivative of g(x)=27x^2-x^3	derivative\:g(x)=27x^{2}-x^{3}
tangent of y=4-9x^2,(-3,-77)	tangent\:y=4-9x^{2},(-3,-77)
integral of (3x)/(x^4+1)	\int\:\frac{3x}{x^{4}+1}dx
slope of 1/(3+2x)	slope\:\frac{1}{3+2x}
inverse oflaplace s/((s+2)(s^2+4))	inverselaplace\:\frac{s}{(s+2)(s^{2}+4)}
(\partial)/(\partial x)(2arctan(x/y))	\frac{\partial\:}{\partial\:x}(2\arctan(\frac{x}{y}))
y^{''''}+20y^{''}+64y=0	y^{\prime\:\prime\:\prime\:\prime\:}+20y^{\prime\:\prime\:}+64y=0
derivative of x^2arctan(6x)	\frac{d}{dx}(x^{2}\arctan(6x))
integral of (24x^2)/(sqrt(100-x^2))	\int\:\frac{24x^{2}}{\sqrt{100-x^{2}}}dx
(dy)/(dx)=112yx^{15}	\frac{dy}{dx}=112yx^{15}
derivative of (x^2/(25))	\frac{d}{dx}(\frac{x^{2}}{25})
derivative of ln(x/(sqrt(x^2+1)))	\frac{d}{dx}(\ln(\frac{x}{\sqrt{x^{2}+1}}))
(\partial)/(\partial x)(msin(2(mx+ny)))	\frac{\partial\:}{\partial\:x}(m\sin(2(mx+ny)))
integral from 2 to e of 1/(xln(x))	\int\:_{2}^{e}\frac{1}{x\ln(x)}dx
derivative of f(x)=x(5x^5-1)	derivative\:f(x)=x(5x^{5}-1)
derivative of \sqrt[3]{t^2}+5sqrt(t^3)	derivative\:\sqrt[3]{t^{2}}+5\sqrt{t^{3}}
integral of xsin(9x^2)	\int\:x\sin(9x^{2})dx
derivative of (x^6/6+1/(16x^4))	\frac{d}{dx}(\frac{x^{6}}{6}+\frac{1}{16x^{4}})
derivative of cos(10x)-1	derivative\:\cos(10x)-1
limit as x approaches 0 of (sin(5x))/(sin(9x))	\lim\:_{x\to\:0}(\frac{\sin(5x)}{\sin(9x)})
integral of x(3x^2-5)	\int\:x(3x^{2}-5)dx
3x^2-2y^3(dy)/(dx)=0	3x^{2}-2y^{3}\frac{dy}{dx}=0
(\partial)/(\partial y)(x^2-y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-y^{2})
integral of x^2+4x+3	\int\:x^{2}+4x+3dx
integral of (sec(x))/(1-tan(x))	\int\:\frac{\sec(x)}{1-\tan(x)}dx
derivative of (x^3-7(2x^2+3))	\frac{d}{dx}((x^{3}-7)(2x^{2}+3))
(sqrt(2x+4))^'	(\sqrt{2x+4})^{\prime\:}
integral from e to 4e of 1/x	\int\:_{e}^{4e}\frac{1}{x}dx
derivative of 12x\sqrt[3]{1-x}sqrt(x+1)	derivative\:12x\sqrt[3]{1-x}\sqrt{x+1}
integral from 0 to ln(3) of e^x-e^{-4x}	\int\:_{0}^{\ln(3)}e^{x}-e^{-4x}dx
(\partial)/(\partial y)(1+y^2sin(2x))	\frac{\partial\:}{\partial\:y}(1+y^{2}\sin(2x))
integral of x(1+x^2)	\int\:x(1+x^{2})dx
derivative of x^3-12x^2+45x	\frac{d}{dx}(x^{3}-12x^{2}+45x)
limit as x approaches 2 of (-2)/0	\lim\:_{x\to\:2}(\frac{-2}{0})
11x-4ysqrt(x^2+1)y^'=0,y(0)=2	11x-4y\sqrt{x^{2}+1}y^{\prime\:}=0,y(0)=2
derivative of e^{x/2} 1/2	\frac{d}{dx}(e^{\frac{x}{2}}\frac{1}{2})
derivative of y=x^2sin^4(x)+xcos^{-6}(x)	derivative\:y=x^{2}\sin^{4}(x)+x\cos^{-6}(x)
derivative of y= 9/(sqrt(x+8))	derivative\:y=\frac{9}{\sqrt{x+8}}
limit as x approaches pi of ((cos(x)+1))/((x-pi)^2)	\lim\:_{x\to\:π}(\frac{(\cos(x)+1)}{(x-π)^{2}})
inverse oflaplace (s^2)/(s^4+2s^2+1)	inverselaplace\:\frac{s^{2}}{s^{4}+2s^{2}+1}
derivative of sqrt(2-7x)	derivative\:\sqrt{2-7x}
integral of 1/(x^2)-3/(x^4)	\int\:\frac{1}{x^{2}}-\frac{3}{x^{4}}dx
laplacetransform 2te^{3t}+4t^2e^{-5t}	laplacetransform\:2te^{3t}+4t^{2}e^{-5t}
derivative of 1/(sqrt(2x-3))	\frac{d}{dx}(\frac{1}{\sqrt{2x-3}})
derivative of 5-4x	derivative\:5-4x
taylor e^{x^5}	taylor\:e^{x^{5}}
integral of sin(x^2)	\int\:\sin(x^{2})dx
integral from 0 to infinity of e^{-3x}	\int\:_{0}^{\infty\:}e^{-3x}dx
integral from 0 to pi/6 of sin(3x)	\int\:_{0}^{\frac{π}{6}}\sin(3x)dx
derivative of sqrt((-x^3+10/4))	\frac{d}{dx}(\sqrt{\frac{-x^{3}+10}{4}})
integral of e^{2sin(3x)}cos(3x)	\int\:e^{2\sin(3x)}\cos(3x)dx
(\partial)/(\partial x)(2y^{1/2}x^{1/2})	\frac{\partial\:}{\partial\:x}(2y^{\frac{1}{2}}x^{\frac{1}{2}})
f(x)=(10)/x	f(x)=\frac{10}{x}
limit as x approaches 2 of (x^2)/(x^2-4)	\lim\:_{x\to\:2}(\frac{x^{2}}{x^{2}-4})
derivative of cos(xdx)	\frac{d}{dx}(\cos(x)dx)
integral of-4sin(2t-pi/2)	\int\:-4\sin(2t-\frac{π}{2})dt
derivative of (xtan(x)/(x^2+1))	\frac{d}{dx}(\frac{x\tan(x)}{x^{2}+1})
derivative of f(x)= 1/(2x+3)	derivative\:f(x)=\frac{1}{2x+3}
y^'+2/x y= 1/(x^2)	y^{\prime\:}+\frac{2}{x}y=\frac{1}{x^{2}}
derivative of (3x^2+2x-1/((1+3x^2)^2))	\frac{d}{dx}(\frac{3x^{2}+2x-1}{(1+3x^{2})^{2}})
y^'=2(t+1)y,y(0)=1	y^{\prime\:}=2(t+1)y,y(0)=1
y^{''}+2*y^'+y=e^{-t}	y^{\prime\:\prime\:}+2\cdot\:y^{\prime\:}+y=e^{-t}
sum from n=0 to infinity of 1/(2^nn!)	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{n}n!}
derivative of f(x)=((x^3+1))/((x^4+1))	derivative\:f(x)=\frac{(x^{3}+1)}{(x^{4}+1)}
limit as x approaches-1 of (x+1)/(x^2-1)	\lim\:_{x\to\:-1}(\frac{x+1}{x^{2}-1})
integral of 2sqrt(4-x^2)	\int\:2\sqrt{4-x^{2}}dx
limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi)	\lim\:_{x\to\:π}(\frac{(e^{\sin(x)}-1)}{x-π})
limit as x approaches-infinity of 7xe^x	\lim\:_{x\to\:-\infty\:}(7xe^{x})

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