2010000306 Level: CEvaluate the following integral on the interval (0;+∞). ∫x3lnxdxx44lnx−x416+c, c∈Rx33lnx−x39+c, c∈Rx22lnx−x24+c, c∈Rxlnx−x+c, c∈R
2010000307 Level: CEvaluate the following integral on R. ∫sin2xcosxdxsin3x3+c, c∈R−cos3xsinx3+c, c∈R2sinx+c, c∈R
9000066001 Level: CIdentify the formula for integration by parts.∫u(x)v′(x)dx=u(x)v(x)−∫u′(x)v(x)dx∫u(x)v(x)dx=u′(x)v′(x)−∫u′(x)v(x)dx∫u′(x)v′(x)dx=u(x)v(x)−∫u′(x)v(x)dx∫u(x)v′(x)dx=u(x)v(x)+∫u′(x)v(x)dx
9000066004 Level: CEvaluate the following integral on R. ∫x2sinxdx−x2cosx+2xsinx+2cosx+c, c∈Rx2cosx−2xsinx−2cosx+c, c∈R13x3cosx+c, c∈R13x3−cosx+c, c∈R
9000066005 Level: CEvaluate the following integral on the interval (0;+∞). ∫lnxdxxlnx−x+c, c∈Rlnx−x+c, c∈Rxlnx+x+c, c∈Rxlnx−12x2+c, c∈R
9000066006 Level: CEvaluate the following integral on the interval (0;+∞). ∫xlnxdx12x2lnx−14x2+c, c∈Rxlnx−12x2+c, c∈Rxlnx−x+c, c∈R12x2+1|x|+c, c∈R
9000066007 Level: CEvaluate the following integral on the interval (0;+∞). ∫x2lnxdx13x3lnx−19x3+c, c∈R12x2lnx−14x2+c, c∈Rxlnx−12x2+c, c∈Rxlnx−x+c, c∈R
9000066009 Level: CEvaluate the following integral on R. ∫x2exdxx2ex−2xex+2ex+c, c∈Rx2ex+2xex−2ex+c, c∈R13x3ex−12x2ex+2ex+c, c∈R13x3ex+12x2ex−2ex+c, c∈R
9000066010 Level: CEvaluate the following integral on R. ∫e2xdx12e2x+c, c∈R13e3x+c, c∈Re2x−ex+c, c∈R2e2x+c, c∈R
9000071208 Level: CEvaluate the following integral on the interval (0;+∞). ∫x2lnxdxx33(lnx−13)+c, c∈Rx23+c, c∈Rx2(xlnx3−12)+c, c∈R