intxcos^(2)xdx=?...

`intxcos^(2)xdx=?`

Text Solution

Verified by Experts

The correct Answer is:

`(1)/(12)xsin3x+(1)/(36)cos3x+(3)/(4)xsinx+(3)/(4)cosx+C`

`cos^(3)x=(1)/(4)cos3x+(3)/(4)cosx`.

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RS AGGARWAL-METHODS OF INTEGRATION -Exercise 13C

Evaluate the following integrals: int2x^(3)e^(x^(2))dx
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Evaluate the following integrals: intxsin^(3)xdx
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intxcos^(2)xdx=?
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Evaluate the following integrals: intx^(3)cosx^(2)dx
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Evaluate the following integrals: intsinxlog(cosx)dx
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Evaluate the following integrals: intxsinxcosxdx
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Evaluate the following integrals: intcossqrt(x)dx
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Evaluate the following integrals: int"cosec"^(3)xdx
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Evaluate the following integrals: intxsin^(3)xcosxdx
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intsinxlog(cosx)dx=?
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Evaluate the following integrals: int(log(logx))/(x)dx
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Evaluate the following integrals: intlog(2+x^(2))dx
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Evaluate the following integrals: int(x)/((1+sinx))dx
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Evaluate the following integrals: int{(1)/(logx)-(1)/((log)^(2))}dx
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Evaluate the following integrals: inte^(x)cos2xcos4xdx
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Evaluate the following integrals: inte^(sqrt(x))dx
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Evaluate the following integrals: inte^(sinx)sin2xdx
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Evaluate the following integrals: int(xsin^(-1)x)/(sqrt(1-x^(2)))dx
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Evaluate the following integrals: int(x^(2)tan^(-1)x)/((1+x^(2)))dx
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Evaluate the following integrals: int(log(x+2))/((x+2)^(2))dx
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