Evaluate the integrals $$\int sin^3x\;cos^6x\;dx$$

Asked by Sakshi | 1 year ago |  159

##### Solution :-

$$\int sin^3x\;cos^6x\;dx$$

=$$∫sin^2x\;sinx\;cos^6xdx$$

=$$∫(1−cos^2x)sinx\;cos^6x\;dx$$

=$$∫(cos^6x−cos^8x)sinx\;dx$$

Let t = cosx

= dt =−sinxdx

$$- \int (t ^6−t ^8)dt$$

$$\dfrac{cos^9x}{9}- \dfrac{cos^7x}{7}+c$$ where t=cosx

Answered by Sakshi | 1 year ago

### Related Questions

#### Evaluate the integrals  \int sin^5x cosx dx

Evaluate the integrals $$\int sin^5x\;cosx\;dx$$

#### Evaluate the integrals \int cos^5xdx

Evaluate the integrals $$\int cos^5xdx$$

#### Evaluate the integrals \int sin^5xdx

Evaluate the integrals $$\int sin^5xdx$$

Evaluate the integrals $$\int sin^4x\;cos^3xdx$$
Evaluate the integrals $$\int cos3x\;cos4x\;dx$$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}